We introduce OneDiffusion, a versatile, large-scale diffusion model that seamlessly supports bidirectional image synthesis and understanding across diverse tasks. It enables conditional generation from inputs such as text, depth, pose, layout, and semantic maps, while also handling tasks like image deblurring, upscaling, and reverse processes such as depth estimation and segmentation. Additionally, OneDiffusion allows for multi-view generation, camera pose estimation, and instant personalization using sequential image inputs. Our model takes a straightforward yet effective approach by treating all tasks as frame sequences with varying noise scales during training, allowing any frame to act as a conditioning image at inference time. Our unified training framework removes the need for specialized architectures, supports scalable multi-task training, and adapts smoothly to any resolution, enhancing both generalization and scalability. Experimental results demonstrate competitive performance across tasks in both generation and prediction such as text-to-image, multiview generation, ID preservation, depth estimation and camera pose estimation despite a relatively small training dataset. Our code and checkpoint are freely available at https://github.com/lehduong/OneDiffusion.

Diffusion models achieve state-of-the-art generation quality across many applications, but their ability to capture rare or extreme events in heavy-tailed distributions remains unclear. In this work, we show that traditional diffusion and flow-matching models with standard Gaussian priors fail to capture heavy-tailed behavior. We address this by repurposing the diffusion framework for heavy-tail estimation using multivariate Student-t distributions. We develop a tailored perturbation kernel and derive the denoising posterior based on the conditional Student-t distribution for the backward process. Inspired by $\gamma$-divergence for heavy-tailed distributions, we derive a training objective for heavy-tailed denoisers. The resulting framework introduces controllable tail generation using only a single scalar hyperparameter, making it easily tunable for diverse real-world distributions. As specific instantiations of our framework, we introduce t-EDM and t-Flow, extensions of existing diffusion and flow models that employ a Student-t prior. Remarkably, our approach is readily compatible with standard Gaussian diffusion models and requires only minimal code changes. Empirically, we show that our t-EDM and t-Flow outperform standard diffusion models in heavy-tail estimation on high-resolution weather datasets in which generating rare and extreme events is crucial.

The site conditions that make astronomical observatories in space and on the ground so desirable---cold and dark---demand a physical remoteness that leads to limited data transmission capabilities. Such transmission limitations directly bottleneck the amount of data acquired and in an era of costly modern observatories, any improvements in lossless data compression has the potential scale to billions of dollars worth of additional science that can be accomplished on the same instrument. Traditional lossless methods for compressing astrophysical data are manually designed. Neural data compression, on the other hand, holds the promise of learning compression algorithms end-to-end from data and outperforming classical techniques by leveraging the unique spatial, temporal, and wavelength structures of astronomical images. This paper introduces [AstroCompress](https://huggingface.co/AstroCompress): a neural compression challenge for astrophysics data, featuring four new datasets (and one legacy dataset) with 16-bit unsigned integer imaging data in various modes: space-based, ground-based, multi-wavelength, and time-series imaging. We provide code to easily access the data and benchmark seven lossless compression methods (three neural and four non-neural, including all practical state-of-the-art algorithms). Our results on lossless compression indicate that lossless neural compression techniques can enhance data collection at observatories, and provide guidance on the adoption of neural compression in scientific applications. Though the scope of this paper is restricted to lossless compression, we also comment on the potential exploration of lossy compression methods in future studies.

Diffusion probabilistic models have achieved mainstream success in many generative modeling tasks, from image generation to inverse problem solving. A distinct feature of these models is that they correspond to deep hierarchical latent variable models optimizing a variational evidence lower bound (ELBO) on the data likelihood. Drawing on a basic connection between likelihood modeling and compression, we explore the potential of diffusion models for progressive coding, resulting in a sequence of bits that can be incrementally transmitted and decoded with progressively improving reconstruction quality. Unlike prior work based on Gaussian diffusion or conditional diffusion models, we propose a new form of diffusion model with uniform noise in the forward process, whose negative ELBO corresponds to the end-to-end compression cost using universal quantization. We obtain promising first results on image compression, achieving competitive rate-distortion-realism results on a wide range of bit-rates with a single model, bringing neural codecs a step closer to practical deployment. Our code can be found at https://github.com/mandt-lab/uqdm.

Diffusion models exhibit excellent sample quality, but existing guidance methods often require additional model training or are limited to specific tasks. We revisit guidance in diffusion models from the perspective of variational inference and control, introducing \emph{Diffusion Trajectory Matching (DTM)} that enables guiding pretrained diffusion trajectories to satisfy a terminal cost. DTM unifies a broad class of guidance methods and enables novel instantiations. We introduce a new method within this framework that achieves state-of-the-art results on several linear, non-linear, and blind inverse problems without requiring additional model training or specificity to pixel or latent space diffusion models. Our code will be available at https://github.com/czi-ai/oc-guidance.

Event sequences appear widely in domains such as medicine, finance, and remote sensing, yet modeling them is challenging due to their heterogeneity: sequences often contain multiple event types with diverse structures—for example, electronic health records that mix discrete events like medical procedures with continuous lab measurements. Existing approaches either tokenize all entries, violating natural inductive biases, or ignore parts of the data to enforce a consistent structure. In this work, we propose a simple yet powerful Marked Temporal Point Process (MTPP) framework for modeling event sequences with flexible structure, using a single unified model. Our approach employs a single autoregressive transformer with discrete and continuous prediction heads, capable of modeling variable-length, mixed-type event sequences. The continuous head leverages an expressive normalizing flow to model continuous event attributes, avoiding the numerical integration required for inter-event times in most competing methods. Empirically, our model excels on both discrete-only and mixed-type sequences, improving prediction quality and enabling interpretable uncertainty quantification. We make our code public at https://github.com/czi-ai/FlexTPP.

Novel view synthesis (NVS) seeks to render photorealistic, 3D‑consistent images of a scene from unseen camera poses given only a sparse set of posed views. Existing deterministic networks render observed regions quickly but blur unobserved areas, whereas stochastic diffusion‑based methods hallucinate plausible content yet incur heavy training‑ and inference‑time costs. In this paper, we propose a hybrid framework that unifies the strengths of both paradigms. A bidirectional transformer encodes multi‑view image tokens and Plücker‑ray embeddings, producing a shared latent representation. Two lightweight heads then act on this representation: (i) a feed‑forward regression head that renders pixels where geometry is well constrained, and (ii) a masked autoregressive diffusion head that completes occluded or unseen regions. The entire model is trained end‑to‑end with joint photometric and diffusion losses, without handcrafted 3D inductive biases, enabling scalability across diverse scenes. Experiments demonstrate that our method attains state‑of‑the‑art image quality while reducing rendering time by an order of magnitude compared with fully generative baselines.

Monitoring chemical processes is essential to prevent catastrophic failures, optimize costs and profits, and ensure the safety of employees and the environment. A key component of modern monitoring systems is the automated detection of anomalies in sensor data over time, called time series, enabling partial automation of plant operation and adding additional layers of supervision to crucial components. The development of anomaly detection methods in this domain is challenging, since real chemical process data are usually proprietary, and simulated data are generally not a sufficient replacement. In this paper, we present NoBOOM, the first collection of datasets for anomaly detection in real-world chemical process data, including labeled data from a running process at our industry partner BASF SE — one of the world’s leading chemical companies — and several chemical processes run in laboratory‑scale and pilot‑scale plants. While we are not able to share every detail about the industrial process, for the laboratory‑ and pilot‑scale plants, we provide comprehensive information on plant configuration, process operation, and, in particular, anomaly events, enabling a differentiated analysis of anomaly detection methods. To demonstrate the complexity of the benchmark, we analyze the data with regard to common issues of time-series anomaly detection (TSAD) benchmarks, including potential triviality and bias.

Diffusion models have recently driven significant breakthroughs in generative modeling. While state-of-the-art models produce high-quality samples on average, individual samples can still be low quality. Detecting such samples without human inspection remains a challenging task. To address this, we propose a Bayesian framework for estimating generative uncertainty of synthetic samples. We outline how to make Bayesian inference practical for large, modern generative models and introduce a new semantic likelihood (evaluated in the latent space of a feature extractor) to address the challenges posed by high-dimensional sample spaces. Through our experiments, we demonstrate that the proposed generative uncertainty effectively identifies poor-quality samples and significantly outperforms existing uncertainty-based methods. Notably, our Bayesian framework can be applied post-hoc to any pretrained diffusion or flow matching model (via the Laplace approximation), and we propose simple yet effective techniques to minimize its computational overhead during sampling.

Modern climate projections lack adequate spatial and temporal resolution due to computational constraints, leading to inaccuracies in representing critical processes like thunderstorms that occur on the sub-resolution scale. Hybrid methods combining physics with machine learning (ML) offer faster, higher fidelity climate simulations by outsourcing compute-hungry, high-resolution simulations to ML emulators. However, these hybrid physics-ML simulations require domain-specific data and workflows that have been inaccessible to many ML experts. This paper is an extended version of our NeurIPS award-winning ClimSim dataset paper. The ClimSim dataset includes 5.7 billion pairs of multivariate input/output vectors spanning ten years at high temporal resolution, capturing the influence of high-resolution, high-fidelity physics on a host climate simulator's macro-scale state. In this extended version, we introduce a significant new contribution in Section 5, which provides a cross-platform, containerized pipeline to integrate ML models into operational climate simulators for hybrid testing. We also implement various baselines of ML models and hybrid simulators to highlight the ML challenges of building stable, skillful emulators. The data (https://huggingface.co/datasets/LEAP/ClimSim_high-res, also in a low-resolution version at https://huggingface.co/datasets/LEAP/ClimSim_low-res and an aquaplanet version at https://huggingface.co/datasets/LEAP/ClimSim_low-res_aqua-planet) and code (https://leap-stc.github.io/ClimSim and https://github.com/leap-stc/climsim-online) are publicly released to support the development of hybrid physics-ML and high-fidelity climate simulations.

Abstract Conformal prediction provides machine learning models with prediction sets that offer theoretical guarantees, but the underlying assumption of exchangeability limits its applicability to time series data. Furthermore, existing approaches struggle to handle multi-step ahead prediction tasks, where uncertainty estimates across multiple future time points are crucial. We propose JANET (Joint Adaptive predictioN-region Estimation for Time-series), a novel framework for constructing conformal prediction regions that are valid for both univariate and multivariate time series. JANET generalises the inductive conformal framework and efficiently produces joint prediction regions with controlled K-familywise error rates, enabling flexible adaptation to specific application needs. Our empirical evaluation demonstrates JANET’s superior performance in multi-step prediction tasks across diverse time series datasets, highlighting its potential for reliable and interpretable uncertainty quantification in sequential data.

Data augmentation plays a critical role in self-supervised learning, including anomaly detection. While hand-crafted transformations such as image rotations can achieve impressive performance on image data, effective transformations of non-image data are lacking. In this work, we study learning such transformations for end-to-end anomaly detection on arbitrary data. We find that a contrastive loss - which encourages learning diverse data transformations while preserving the relevant semantic content of the data - is more suitable than previously proposed losses for transformation learning, a fact that we prove theoretically and empirically. We demonstrate that anomaly detection using neural transformation learning can achieve state-of-the-art results for time series data, tabular data, text data and graph data. Furthermore, our approach can make image anomaly detection more interpretable by learning transformations at different levels of abstraction.

Diffusion models suffer from slow sample generation at inference time. Therefore, developing a principled framework for fast deterministic/stochastic sampling for a broader class of diffusion models is a promising direction. We propose two complementary frameworks for accelerating sample generation in pre-trained models: Conjugate Integrators and Splitting Integrators. Conjugate integrators generalize DDIM, mapping the reverse diffusion dynamics to a more amenable space for sampling. In contrast, splitting-based integrators, commonly used in molecular dynamics, reduce the numerical simulation error by cleverly alternating between numerical updates involving the data and auxiliary variables. After extensively studying these methods empirically and theoretically, we present a hybrid method that leads to the best-reported performance for diffusion models in augmented spaces. Applied to Phase Space Langevin Diffusion [Pandey \& Mandt, 2023] on CIFAR-10, our deterministic and stochastic samplers achieve FID scores of 2.11 and 2.36 in only 100 network function evaluations (NFE) as compared to 2.57 and 2.63 for the best-performing baselines, respectively. Our code and model checkpoints will be made publicly available at https://github.com/mandt-lab/PSLD

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

Neural Radiance Fields (NeRFs) have emerged as powerful tools for capturing detailed 3D scenes through continuous volumetric representations. Recent NeRFs utilize feature grids to improve rendering quality and speed; however, these representations introduce significant storage overhead. This paper presents a novel method for efficiently compressing a grid-based NeRF model, addressing the storage overhead concern. Our approach is based on the non-linear transform coding paradigm, employing neural compression for compressing the model's feature grids. Due to the lack of training data involving many i.i.d scenes, we design an encoder-free, end-to-end optimized approach for individual scenes, using lightweight decoders. To leverage the spatial inhomogeneity of the latent feature grids, we introduce an importance-weighted rate-distortion objective and a sparse entropy model employing a masking mechanism. Our experimental results validate that our proposed method surpasses existing works in terms of grid-based NeRF compression efficacy and reconstruction quality.

In climate science and meteorology, high-resolution local precipitation (rain and snowfall) predictions are limited by the computational costs of simulation-based methods. Statistical downscaling, or super-resolution, is a common workaround where a low-resolution prediction is improved using statistical approaches. Unlike traditional computer vision tasks, weather and climate applications require capturing the accurate conditional distribution of high-resolution given low-resolution patterns to assure reliable ensemble averages and unbiased estimates of extreme events, such as heavy rain. This work extends recent video diffusion models to precipitation super-resolution, employing a deterministic downscaler followed by a temporally-conditioned diffusion model to capture noise characteristics and high-frequency patterns. We test our approach on FV3GFS output, an established large-scale global atmosphere model, and compare it against six state-of-the-art baselines. Our analysis, capturing CRPS, MSE, precipitation distributions, and qualitative aspects using California and the Himalayas as examples, establishes our method as a new standard for data-driven precipitation downscaling.

Constructing fast samplers for unconditional diffusion and flow-matching models has received much attention recently; however, existing methods for solving *inverse problems*, such as super-resolution, inpainting, or deblurring, still require hundreds to thousands of iterative steps to obtain high-quality results. We propose a plug-and-play framework for constructing efficient samplers for inverse problems, requiring only *pre-trained* diffusion or flow-matching models. We present *Conditional Conjugate Integrators*, which leverage the specific form of the inverse problem to project the respective conditional diffusion/flow dynamics into a more amenable space for sampling. Our method complements popular posterior approximation methods for solving inverse problems using diffusion/flow models. We evaluate the proposed method's performance on various linear image restoration tasks across multiple datasets, employing diffusion and flow-matching models. Notably, on challenging inverse problems like 4x super-resolution on the ImageNet dataset, our method can generate high-quality samples in as few as *5* conditional sampling steps and outperforms competing baselines requiring 20-1000 steps. Our code will be publicly available at https://github.com/mandt-lab/c-pigdm.

Variational Autoencoders for multimodal data hold promise for many tasks in data analysis, such as representation learning, conditional generation, and imputation. Current architectures either share the encoder output, decoder input, or both across modalities to learn a shared representation. Such architectures impose hard constraints on the model. In this work, we show that a better latent representation can be obtained by replacing these hard constraints with a soft constraint. We propose a new mixture-of-experts prior, softly guiding each modality's latent representation towards a shared aggregate posterior. This approach results in a superior latent representation and allows each encoding to preserve information better from its uncompressed original features. In extensive experiments on multiple benchmark datasets and two challenging real-world datasets, we show improved learned latent representations and imputation of missing data modalities compared to existing methods.

Early-exit neural networks (EENNs) facilitate adaptive inference by producing predictions at multiple stages of the forward pass. In safety-critical applications, these predictions are only meaningful when complemented with reliable uncertainty estimates. Yet, due to their sequential structure, an EENN’s uncertainty estimates should also be *consistent*: labels that are deemed improbable at one exit should not reappear within the confidence interval / set of later exits. We show that standard uncertainty quantification techniques, like Bayesian methods or conformal prediction, can lead to inconsistency across exits. We address this problem by applying anytime-valid confidence sequences (AVCSs) to the exits of EENNs. By design, AVCSs maintain consistency across exits. We examine the theoretical and practical challenges of applying AVCSs to EENNs and empirically validate our approach on both regression and classification tasks.

Deep, overparameterized regression models are notorious for their tendency to overfit. This problem is exacerbated in heteroskedastic models, which predict both mean and residual noise for each data point. At one extreme, these models fit all training data perfectly, eliminating residual noise entirely; at the other, they overfit the residual noise while predicting a constant, uninformative mean. We observe a lack of middle ground, suggesting a phase transition dependent on model regularization strength. Empirical verification supports this conjecture by fitting numerous models with varying mean and variance regularization. To explain the transition, we develop a theoretical framework based on a statistical field theory, yielding qualitative agreement with experiments. As a practical consequence, our analysis simplifies hyperparameter tuning from a two-dimensional to a one-dimensional search, substantially reducing the computational burden. Experiments on diverse datasets, including UCI datasets and the large-scale ClimSim climate dataset, demonstrate significantly improved performance in various calibration tasks.

Continuous-time event sequences, i.e., sequences consisting of continuous time stamps and associated event types (“marks”), are an important type of sequential data with many applications, e.g., in clinical medicine or user behavior modeling. Since these data are typically modeled in an autoregressive manner (e.g., using neural Hawkes processes or their classical counterparts), it is natural to ask questions about future scenarios such as “what kind of event will occur next” or “will an event of type $A$ occur before one of type $B$.” Addressing such queries with direct methods such as naive simulation can be highly inefficient from a computational perspective. This paper introduces a new typology of query types and a framework for addressing them using importance sampling. Example queries include predicting the $n^\mathrm{th}$ event type in a sequence and the hitting time distribution of one or more event types. We also leverage these findings further to be applicable for estimating general “$A$ before $B$” type of queries. We prove theoretically that our estimation method is effectively always better than naive simulation and demonstrate empirically based on three real-world datasets that our approach can produce orders of magnitude improvements in sampling efficiency compared to naive methods.

Score-based Generative Models (SGMs) have demonstrated exceptional synthesis outcomes across various tasks. However, the current design landscape of the forward diffusion process remains largely untapped and often relies on physical heuristics or simplifying assumptions. Utilizing insights from the development of scalable Bayesian posterior samplers, we present a complete recipe for formulating forward processes in SGMs, ensuring convergence to the desired target distribution. Our approach reveals that several existing SGMs can be seen as specific manifestations of our framework. Building upon this method, we introduce Phase Space Langevin Diffusion (PSLD), which relies on score-based modeling within an augmented space enriched by auxiliary variables akin to physical phase space. Empirical results exhibit the superior sample quality and improved speed-quality trade-off of PSLD compared to various competing approaches on established image synthesis benchmarks. Remarkably, PSLD achieves sample quality akin to state-ofthe-art SGMs (FID: 2.10 for unconditional CIFAR-10 generation). Lastly, we demonstrate the applicability of PSLD in conditional synthesis using pre-trained score networks, offering an appealing alternative as an SGM backbone for future advancements. Code and model checkpoints can be accessed at https://github.com/mandt-lab/PSLD.

Neural image compression methods have seen increasingly strong performance in recent years. However, they suffer orders of magnitude higher computational complexity compared to traditional codecs, which hinders their real-world deployment. This paper takes a step forward in closing this gap in decoding complexity by adopting shallow or even linear decoding transforms. To compensate for the resulting drop in compression performance, we exploit the often asymmetrical computation budget between encoding and decoding, by adopting more powerful encoder networks and iterative encoding. We theoretically formalize the intuition behind, and our experimental results establish a new frontier in the trade-off between rate-distortion and decoding complexity for neural image compression. Specifically, we achieve rate-distortion performance competitive with the established mean-scale hyperprior architecture of Minnen et al. (2018) at less than 50K decoding FLOPs/pixel, reducing the baseline’s overall decoding complexity by 80%, or over 90% for the synthesis transform alone. Our code can be found at https://github.com/mandt-lab/shallow-ntc.

Selecting informative data points for expert feedback can significantly improve the performance of anomaly detection (AD) in various contexts, such as medical diagnostics or fraud detection. In this paper, we determine a set of theoretical conditions under which anomaly scores generalize from labeled queries to unlabeled data. Motivated by these results, we propose a data labeling strategy with optimal data coverage under labeling budget constraints. In addition, we propose a new learning framework for semi-supervised AD. Extensive experiments on image, tabular, and video data sets show that our approach results in state-of-the-art semi-supervised AD performance under labeling budget constraints.

We present a fully Bayesian autoencoder model that treats both local latent variables and global decoder parameters in a Bayesian fashion. This approach allows for flexible priors and posterior approximations while keeping the inference costs low. To achieve this, we introduce an amortized MCMC approach by utilizing an implicit stochastic network to learn sampling from the posterior over local latent variables. Furthermore, we extend the model by incorporating a Sparse Gaussian Process prior over the latent space, allowing for a fully Bayesian treatment of inducing points and kernel hyperparameters and leading to improved scalability. Additionally, we enable Deep Gaussian Process priors on the latent space and the handling of missing data. We evaluate our model on a range of experiments focusing on dynamic representation learning and generative modeling, demonstrating the strong performance of our approach in comparison to existing methods that combine Gaussian Processes and autoencoders.

Anomaly detection (AD) plays a crucial role in many safety-critical application domains. The challenge of adapting an anomaly detector to drift in the normal data distribution, especially when no training data is available for the "new normal," has led to the development of zero-shot AD techniques. In this paper, we propose a simple yet effective method called Adaptive Centered Representations (ACR) for zero-shot batch-level AD. Our approach trains off-the-shelf deep anomaly detectors (such as deep SVDD) to adapt to a set of inter-related training data distributions in combination with batch normalization, enabling automatic zero-shot generalization for unseen AD tasks. This simple recipe, batch normalization plus meta-training, is a highly effective and versatile tool. Our results demonstrate the first zero-shot AD results for tabular data and outperform existing methods in zero-shot anomaly detection and segmentation on image data from specialized domains.

In the theory of lossy compression, the rate-distortion (R-D) function $R(D)$ describes how much a data source can be compressed (in bit-rate) at any given level of fidelity (distortion). Obtaining $R(D)$ for a given data source establishes the fundamental performance limit for all compression algorithms. We propose a new method to estimate $R(D)$ from the perspective of optimal transport. Unlike the classic Blahut--Arimoto algorithm which fixes the support of the reproduction distribution in advance, our Wasserstein gradient descent algorithm learns the support of the optimal reproduction distribution by moving particles. We prove its local convergence and analyze the sample complexity of our R-D estimator based on a connection to entropic optimal transport. Experimentally, we obtain comparable or tighter bounds than state-of-the-art neural network methods on low-rate sources while requiring considerably less tuning and computation effort. We also highlight a connection to maximum-likelihood deconvolution and introduce a new class of sources that can be used as test cases with known solutions to the R-D problem.

This paper outlines an end-to-end optimized lossy image compression framework using diffusion generative models. The approach relies on the transform coding paradigm, where an image is mapped into a latent space for entropy coding and, from there, mapped back to the data space for reconstruction. In contrast to VAE-based neural compression, where the (mean) decoder is a deterministic neural network, our decoder is a conditional diffusion model. Our approach thus introduces an additional "content" latent variable on which the reverse diffusion process is conditioned and uses this variable to store information about the image. The remaining ``texture'' variables characterizing the diffusion process are synthesized at decoding time. We show that the model's performance can be tuned toward perceptual metrics of interest. Our extensive experiments involving multiple datasets and image quality assessment metrics show that our approach yields stronger reported FID scores than the GAN-based model, while also yielding competitive performance with VAE-based models in several distortion metrics. Furthermore, training the diffusion with $\mathcal{X}$-parameterization enables high-quality reconstructions in only a handful of decoding steps, greatly affecting the model's practicality. Our code is available at: https://github.com/buggyyang/CDC_compression

Modern climate projections lack adequate spatial and temporal resolution due to computational constraints. A consequence is inaccurate and imprecise predictions of critical processes such as storms. Hybrid methods that combine physics with machine learning (ML) have introduced a new generation of higher fidelity climate simulators that can sidestep Moore's Law by outsourcing compute-hungry, short, high-resolution simulations to ML emulators. However, this hybrid ML-physics simulation approach requires domain-specific treatment and has been inaccessible to ML experts because of lack of training data and relevant, easy-to-use workflows. We present ClimSim, the largest-ever dataset designed for hybrid ML-physics research. It comprises multi-scale climate simulations, developed by a consortium of climate scientists and ML researchers. It consists of 5.7 billion pairs of multivariate input and output vectors that isolate the influence of locally-nested, high-resolution, high-fidelity physics on a host climate simulator's macro-scale physical state.The dataset is global in coverage, spans multiple years at high sampling frequency, and is designed such that resulting emulators are compatible with downstream coupling into operational climate simulators. We implement a range of deterministic and stochastic regression baselines to highlight the ML challenges and their scoring. The data (https://huggingface.co/datasets/LEAP/ClimSim_high-res) and code (https://leap-stc.github.io/ClimSim) are released openly to support the development of hybrid ML-physics and high-fidelity climate simulations for the benefit of science and society.

Marked temporal point processes (MTPPs) are a general class of stochastic models for modeling the evolution of events of different types (“marks”) in continuous time. These models have broad applications in areas such as medical data monitoring, financial prediction, user modeling, and communication networks. Of significant practical interest in such problems is the issue of missing or censored data over time. In this paper, we focus on the specific problem of inference for a trained MTPP model when events of certain types are not observed over a period of time during prediction. We introduce the concept of mark-censored sub-processes and use this framework to develop a novel marginalization technique for inference in the presence of censored marks. The approach is model-agnostic and applicable to any MTPP model with a well-defined intensity function. We illustrate the flexibility and utility of the method in the context of both parametric and neural MTPP models, with results across a range of datasets including data from simulated Hawkes processes, self-correcting processes, and multiple real-world event datasets.

While recent machine learning research has revealed connections between deep generative models such as VAEs and rate-distortion losses used in learned compression, most of this work has focused on images. In a similar spirit, we view recently proposed neural video coding algorithms through the lens of deep autoregressive and latent variable modeling. We present these codecs as instances of a generalized stochastic temporal autoregressive transform, and propose new avenues for further improvements inspired by normalizing flows and structured priors. We propose several architectures that yield state-of-the-art video compression performance on high-resolution video and discuss their tradeoffs and ablations. In particular, we propose (i) improved temporal autoregressive transforms, (ii) improved entropy models with structured and temporal dependencies, and (iii) variable bitrate versions of our algorithms. Since our improvements are compatible with a large class of existing models, we provide further evidence that the generative modeling viewpoint can advance the neural video coding field.

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is a scalable algorithm for asymptotically exact Bayesian inference in parameter-rich models, such as Bayesian neural networks. However, since mixing can be slow in high dimensions, practitioners often resort to variational inference (VI). Unfortunately, VI makes strong assumptions on both the factorization and functional form of the posterior. To relax these assumptions, this work proposes a new non-parametric variational inference scheme that combines ideas from both SGMCMC and coordinate-ascent VI. The approach relies on a new Langevin-type algorithm that operates on a "self-averaged" posterior energy function, where parts of the latent variables are averaged over samples from earlier iterations of the Markov chain. This way, statistical dependencies between coordinates can be broken in a controlled way, allowing the chain to mix faster. This scheme can be further modified in a "dropout" manner, leading to even more scalability. We test our scheme for ResNet-20 on CIFAR-10, SVHN, and FMNIST. In all cases, we find improvements in convergence speed and/or final accuracy compared to SGMCMC and parametric VI.

Anomaly detection aims at identifying data points that show systematic deviations from the majority of data in an unlabeled dataset. A common assumption is that clean training data (free of anomalies) is available, which is often violated in practice. We propose a strategy for training an anomaly detector in the presence of unlabeled anomalies that is compatible with a broad class of models. The idea is to jointly infer binary labels to each datum (normal vs. anomalous) while updating the model parameters. Inspired by outlier exposure (Hendrycks et al., 2018) that considers synthetically created, labeled anomalies, we thereby use a combination of two losses that share parameters: one for the normal and one for the anomalous data. We then iteratively proceed with block coordinate updates on the parameters and the most likely (latent) labels. Our experiments with several backbone models on three image datasets, 30 tabular data sets, and a video anomaly detection benchmark showed consistent and significant improvements over the baselines.

Graph-level anomaly detection has become a critical topic in diverse areas, such as financial fraud detection and detecting anomalous activities in social networks. While most research has focused on anomaly detection for visual data such as images, where high detection accuracies have been obtained, existing deep learning approaches for graphs currently show considerably worse performance. This paper raises the bar on graph-level anomaly detection, i.e., the task of detecting abnormal graphs in a set of graphs. By drawing on ideas from self-supervised learning and transformation learning, we present a new deep learning approach that significantly improves existing deep one-class approaches by fixing some of their known problems, including hypersphere collapse and performance flip. Experiments on nine real-world data sets involving nine techniques reveal that our method achieves an average performance improvement of 11.8% AUC compared to the best existing approach.

In reasoning about sequential events it is natural to pose probabilistic queries such as “when will event A occur next” or “what is the probability of A occurring before B”, with applications in areas such as user modeling, language models, medicine, and finance. These types of queries are complex to answer compared to next-event prediction, particularly for neural autoregressive models such as recurrent neural networks and transformers. This is in part due to the fact that future querying involves marginalization over large path spaces, which is not straightforward to do efficiently in such models. In this paper we introduce a general typology for predictive queries in neural autoregressive sequence models and show that such queries can be systematically represented by sets of elementary building blocks. We leverage this typology to develop new query estimation methods based on beam search, importance sampling, and hybrids. Across four large-scale sequence datasets from different application domains, as well as for the GPT-2 language model, we demonstrate the ability to make query answering tractable for arbitrary queries in exponentially-large predictive path-spaces, and find clear differences in cost-accuracy tradeoffs between search and sampling methods.

There has been much interest in deploying deep learning algorithms on low-powered devices, including smart-phones, drones, and medical sensors. However, full-scale deep neural networks are often too resource-intensive in terms of energy and storage. As a result, the bulk part of the machine learning operation is therefore often carried out on an edge server, where the data is compressed and transmitted. However, compressing data (such as images) leads to transmitting information irrelevant to the supervised task. Another popular approach is to split the deep network between the device and the server while compressing intermediate features. To date, however, such split computing strategies have barely outperformed the aforementioned naive data compression baselines due to their inefficient approaches to feature compression. This paper adopts ideas from knowledge distillation and neural image compression to compress intermediate feature representations more efficiently. Our supervised compression approach uses a teacher model and a student model with a stochastic bottleneck and learnable prior for entropy coding (Entropic Student). We compare our approach to various neural image and feature compression baselines in three vision tasks and found that it achieves better supervised rate-distortion performance while maintaining smaller end-to-end latency. We furthermore show that the learned feature representations can be tuned to serve multiple downstream tasks.

Conventional variational autoencoders fail in modeling correlations between data points due to their use of factorized priors. Amortized Gaussian process inference through GP-VAEs has led to significant improvements in this regard, but is still inhibited by the intrinsic complexity of exact GP inference. We improve the scalability of these methods through principled sparse inference approaches. We propose a new scalable GP-VAE model that outperforms existing approaches in terms of runtime and memory footprint, is easy to implement, and allows for joint end-to-end optimization of all components.

Data transformations (e.g. rotations, reflections, and cropping) play an important role in self-supervised learning. Typically, images are transformed into different views, and neural networks trained on tasks involving these views produce useful feature representations for downstream tasks, including anomaly detection. However, for anomaly detection beyond image data, it is often unclear which transformations to use. Here we present a simple end-to-end procedure for anomaly detection with learnable transformations. The key idea is to embed the transformed data into a semantic space such that the transformed data still resemble their untransformed form, while different transformations are easily distinguishable. Extensive experiments on time series show that our proposed method outperforms existing approaches in the one-vs.-rest setting and is competitive in the more challenging n-vs.-rest anomaly-detection task. On medical and cyber-security tabular data, our method learns domain-specific transformations and detects anomalies more accurately than previous work.

We consider the problem of online learning in the presence of distribution shifts that occur at an unknown rate and of unknown intensity. We derive a new Bayesian online inference approach to simultaneously infer these distribution shifts and adapt the model to the detected changes by integrating ideas from change point detection, switching dynamical systems, and Bayesian online learning. Using a binary ‘change variable,’ we construct an informative prior such that--if a change is detected--the model partially erases the information of past model updates by tempering to facilitate adaptation to the new data distribution. Furthermore, the approach uses beam search to track multiple change-point hypotheses and selects the most probable one in hindsight. Our proposed method is model-agnostic, applicable in both supervised and unsupervised learning settings, suitable for an environment of concept drifts or covariate drifts, and yields improvements over state-of-the-art Bayesian online learning approaches.

Multivariate time series with missing values are common in areas such as healthcare and finance, and have grown in number and complexity over the years. This raises the question whether deep learning methodologies can outperform classical data imputation methods in this domain. However, naive applications of deep learning fall short in giving reliable confidence estimates and lack interpretability.We propose a new deep sequential latent variable model for dimensionality reduction and data imputation. Our modeling assumption is simple and interpretable: the high dimensional time series has a lower-dimensional representation which evolves smoothly in time according to a Gaussian process. The non-linear dimensionality reduction in the presence of missing data is achieved using a VAE approach with a novel structured variational approximation. We demonstrate that our approach outperforms both classical and recent deep learning-based data imputation methods on high dimensional data from the domains of computer vision and healthcare.

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the approximate posterior in the hope of improving performance. In contrast, here we share a curious experimental finding that suggests instead restricting the variational distribution to a more compact parameterization. For a variety of deep Bayesian neural networks trained using Gaussian mean-field variational inference, we find that the posterior standard deviations consistently exhibit strong low-rank structure after convergence. This means that by decomposing these variational parameters into a low-rank factorization, we can make our variational approximation more compact without decreasing the models’ performance. Furthermore, we find that such factorized parameterizations improve the signal-to-noise ratio of stochastic gradient estimates of the variational lower bound, resulting in faster convergence.

During the past five years the Bayesian deep learning community has developed increasingly accurate and efficient approximate inference procedures that allow for Bayesian inference in deep neural networks. However, despite this algorithmic progress and the promise of improved uncertainty quantification and sample efficiency there are—as of early 2020—no publicized deployments of Bayesian neural networks in industrial practice. In this work we cast doubt on the current understanding of Bayes posteriors in popular deep neural networks: we demonstrate through careful MCMC sampling that the posterior predictive induced by the Bayes posterior yields systematically worse predictions when compared to simpler methods including point estimates obtained from SGD. Furthermore, we demonstrate that predictive performance is improved significantly through the use of a “cold posterior” that overcounts evidence. Such cold posteriors sharply deviate from the Bayesian paradigm but are commonly used as heuristic in Bayesian deep learning papers. We put forward several hypotheses that could explain cold posteriors and evaluate the hypotheses through experiments. Our work questions the goal of accurate posterior approximations in Bayesian deep learning: If the true Bayes posterior is poor, what is the use of more accurate approximations? Instead, we argue that it is timely to focus on understanding the origin of cold posteriors.

We propose a novel algorithm for quantizing continuous latent representations in trained models. Our approach applies to deep probabilistic models, such as variational autoencoders (VAEs), and enables both data and model compression. Unlike current end-to-end neural compression methods that cater the model to a fixed quantization scheme, our algorithm separates model design and training from quantization. Consequently, our algorithm enables “plug-and-play” compression with variable rate-distortion trade-off, using a single trained model. Our algorithm can be seen as a novel extension of arithmetic coding to the continuous domain, and uses adaptive quantization accuracy based on estimates of posterior uncertainty. Our experimental results demonstrate the importance of taking into account posterior uncertainties, and show that image compression with the proposed algorithm outperforms JPEG over a wide range of bit rates using only a single standard VAE. Further experiments on Bayesian neural word embeddings demonstrate the versatility of the proposed method.

Continuous-time event data are common in applications such as individual behavior data, financial transactions, and medical health records. Modeling such data can be very challenging, in particular for applications with many different types of events,since it requires a model to predict the event types as well as the time of occurrence. Recurrent neural networks that parameterize time-varying intensity functions are the current state-of-the-art for predictive modeling with such data. These models typically assume that all event sequences come from the same data distribution. However, in many applications event sequences are generated by different sources,or users, and their characteristics can be very different. In this paper, we extend the broad class of neural marked point process models to mixtures of latent embeddings,where each mixture component models the characteristic traits of a given user. Our approach relies on augmenting these models with a latent variable that encodes user characteristics, represented by a mixture model over user behavior that is trained via amortized variational inference. We evaluate our methods on four large real-world datasets and demonstrate systematic improvements from our approach over existing work for a variety of predictive metrics such as log-likelihood, next event ranking, and source-of-sequence identification.

We consider the problem of lossy image compression with deep latent variable models. State-of-the-art methods build on hierarchical variational autoencoders (VAEs) and learn inference networks to predict a compressible latent representation of each data point. Drawing on the variational inference perspective on compression, we identify three approximation gaps which limit performance in the conventional approach: an amortization gap, a discretization gap, and a marginalization gap. We propose remedies for each of these three limitations based on ideas related to iterative inference, stochastic annealing for discrete optimization, and bits-back coding, resulting in the first application of bits-back coding to lossy compression. In our experiments, which include extensive baseline comparisons and ablation studies, we achieve new state-of-the-art performance on lossy image compression using an established VAE architecture, by changing only the inference method.

The convergence speed of stochastic gradient descent (SGD) can be improved by actively selecting mini-batches. We explore sampling schemes where similar data points are less likely to be selected in the same mini-batch. In particular, we prove that such repulsive sampling schemes lower the variance of the gradient estimator. This generalizes recent work on using Determinantal Point Processes (DPPs) for mini-batch diversification (Zhang et al., 2017) to the broader class of repulsive point processes. We first show that the phenomenon of variance reduction by diversified sampling generalizes in particular to non-stationary point processes. We then show that other point processes may be computationally much more efficient than DPPs. In particular, we propose and investigate Poisson Disk sampling—frequently encountered in the computer graphics community—for this task. We show empirically that our approach improves over standard SGD both in terms of convergence speed as well as final model performance.

Florian Schmidt, Stephan Mandt, Thomas Hofmann. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP). 2019.

Robotic painting is well-established in controlled factory environments, but there is now potential for mobile robots to do functional painting tasks around the everyday world. An obvious first target for such robots is painting a uniform single color. A step further is the painting of textured images. Texture involves a varying appearance, and requires that paint is delivered accurately onto the physical surface to produce the desired effect. Robotic painting of texture is relevant for architecture and in themed environments.A key challenge for robotic painting of texture is to take a desired image as input, and to generate the paint commands to as closely as possible create the desired appearance, according to the robotic capabilities. This paper describes a deep learning approach to take an input ink map of a desired texture, and infer robotic paint commands to produce that texture.We analyze the trade-offs between quality of reconstructed appearance and ease of execution. Our method is general for different kinds of robotic paint delivery systems, but the emphasis here is on spray painting. More generally, the framework can be viewed as an approach for solving a specific class of inverse imaging problems.

The usage of deep generative models for image compression has led to impressive performance gains over classical codecs while neural video compression is still in its infancy. Here, we propose an end-to-end, deep generative modeling approach to compress temporal sequences with a focus on video. Our approach builds upon variational autoencoder (VAE) models for sequential data and combines them with recent work on neural image compression. The approach jointly learns to transform the original sequence into a lower-dimensional representation as well as to discretize and entropy code this representation according to predictions of the sequential VAE. Rate-distortion evaluations on small videos from public data sets with varying complexity and diversity show that our model yields competitive results when trained on generic video content. Extreme compression performance is achieved when training the model on specialized content.

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solving an optimization problem. This approach has been successfully applied to various models and large-scale applications. In this review, we give an overview of recent trends in variational inference. We first introduce standard mean field variational inference, then review recent advances focusing on the following aspects: (a) scalable VI, which includes stochastic approximations, (b) generic VI, which extends the applicability of VI to a large class of otherwise intractable models, such as non-conjugate models, (c) accurate VI, which includes variational models beyond the mean field approximation or with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. Finally, we provide a summary of promising future research directions.

Dynamic topic models (DTMs) model the evolution of prevalent themes in literature, online media, and other forms of text over time. DTMs assume that word co-occurrence statistics change continuously and therefore impose continuous stochastic process priors on their model parameters. These dynamical priors make inference much harder than in regular topic models, and also limit scalability. In this paper, we present several new results around DTMs. First, we extend the class of tractable priors from Wiener processes to the generic class of Gaussian processes (GPs). This allows us to explore topics that develop smoothly over time, that have a long-term memory or are temporally concentrated (for event detection). Second, we show how to perform scalable approximate inference in these models based on ideas around stochastic variational inference and sparse Gaussian processes. This way we can train a rich family of DTMs to massive data. Our experiments on several large-scale datasets show that our generalized model allows us to find interesting patterns that were not accessible by previous approaches.

Word embeddings have become a mainstream tool in statistical natural language processing.Practitioners often use pre-trained word vectors, which were trained on large generic text corpora, and which are readily available on the web.However, pre-trained word vectors oftentimes lack important words from specific domains.It is therefore often desirable to extend the vocabulary and embed new words into a set of pre-trained word vectors.In this paper, we present an efficient method for including new words from a specialized corpus, containing new words, into pre-trained generic word embeddings.We build on the established view of word embeddings as matrix factorizations to present a spectral algorithm for this task.Experiments on several domain-specific corpora with specialized vocabularies demonstrate that our method is able to embed the new words efficiently into the original embedding space.Compared to competing methods, our method is faster, parameter-free, and deterministic.

Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic gradients. We propose variance reduction by means of Quasi-Monte Carlo (QMC) sampling. QMC replaces N i.i.d. samples from a uniform probability distribution by a deterministic sequence of samples of length N. This sequence covers the underlying random variable space more evenly than i.i.d. draws, reducing the variance of the gradient estimator. With our novel approach, both the score function and the reparameterization gradient estimators lead to much faster convergence. We also propose a new algorithm for Monte Carlo objectives, where we operate with a constant learning rate and increase the number of QMC samples per iteration. We prove that this way, our algorithm can converge asymptotically at a faster rate than SGD . We furthermore provide theoretical guarantees on qmc for Monte Carlo objectives that go beyond MCVI , and support our findings by several experiments on large-scale data sets from various domains.

We present a VAE architecture for encoding and generating high dimensional sequential data, such as video or audio. Our deep generative model learns a latent representation of the data which is split into a static and dynamic part, allowing us to approximately disentangle latent time-dependent features (dynamics) from features which are preserved over time (content). This architecture gives us partial control over generating content and dynamics by conditioning on either one of these sets of features. In our experiments on artificially generated cartoon video clips and voice recordings, we show that we can convert the content of a given sequence into another one by such content swapping. For audio, this allows us to convert a male speaker into a female speaker and vice versa, while for video we can separately manipulate shapes and dynamics. Furthermore, we give empirical evidence for the hypothesis that stochastic RNNs as latent state models are more efficient at compressing and generating long sequences than deterministic ones, which may be relevant for applications in video compression.

Inference models are a key component in scaling variational inference to deep latent variable models, most notably as encoder networks in variational auto-encoders (VAEs). By replacing conventional optimization-based inference with a learned model, inference is amortized over data examples and therefore more computationally efficient. However, standard inference models are restricted to direct mappings from data to approximate posterior estimates. The failure of these models to reach fully optimized approximate posterior estimates results in an amortization gap. We aim toward closing this gap by proposing iterative inference models, which learn to perform inference optimization through repeatedly encoding gradients. Our approach generalizes standard inference models in VAEs and provides insight into several empirical findings, including top-down inference techniques. We demonstrate the inference optimization capabilities of iterative inference models and show that they outperform standard inference models on several benchmark data sets of images and text.

Matrix and tensor factorization methods are often used for finding underlying low-dimensional patterns from noisy data. In this paper, we study non-linear tensor factorization methods based on deep variational autoencoders. Our approach is well-suited for settings where the relationship between the latent representation to be learned and the raw data representation is highly complex. We apply our approach to a large dataset of facial expressions of movie-watching audiences (over 16 million faces). Our experiments show that compared to conventional linear factorization methods, our method achieves better reconstruction of the data, and further discovers interpretable latent factors.

We present a probabilistic language model for time-stamped text data which tracks the semantic evolution of individual words over time. The model represents words and contexts by latent trajectories in an embedding space. At each moment in time, the embedding vectors are inferred from a probabilistic version of word2vec [Mikolov et al., 2013]. These embedding vectors are connected in time through a latent diffusion process. We describe two scalable variational inference algorithms–skip-gram smoothing and skip-gram filtering–that allow us to train the model jointly over all times; thus learning on all data while simultaneously allowing word and context vectors to drift. Experimental results on three different corpora demonstrate that our dynamic model infers word embedding trajectories that are more interpretable and lead to higher predictive likelihoods than competing methods that are based on static models trained separately on time slices.

Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with generalized divergences as a form of estimating the marginal likelihood via biased importance sampling. The choice of divergence determines a bias-variance trade-off between the tightness of a bound on the marginal likelihood (low bias) and the variance of its gradient estimators. Drawing on variational perturbation theory of statistical physics, we use these insights to construct a family of new variational bounds. Enumerated by an odd integer order $K$, this family captures the standard KL bound for $K=1$, and converges to the exact marginal likelihood as $K\to\infty$. Compared to alpha-divergences, our reparameterization gradients have a lower variance. We show in experiments on Gaussian Processes and Variational Autoencoders that the new bounds are more mass covering, and that the resulting posterior covariances are closer to the true posterior and lead to higher likelihoods on held-out data.

Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an approximate Bayesian posterior inference algorithm. Specifically, we show how to adjust the tuning parameters of constant SGD to best match the stationary distribution to a posterior, minimizing the Kullback-Leibler divergence between these two distributions. (2) We demonstrate that constant SGD gives rise to a new variational EM algorithm that optimizes hyperparameters in complex probabilistic models. (3) We also show how to tune SGD with momentum for approximate sampling. (4) We analyze stochastic-gradient MCMC algorithms. For Stochastic- Gradient Langevin Dynamics and Stochastic-Gradient Fisher Scoring, we quantify the approximation errors due to finite learning rates. Finally (5), we use the stochastic process perspective to give a short proof of why Polyak averaging is optimal. Based on this idea, we propose a scalable approximate MCMC algorithm, the Averaged Stochastic Gradient Sampler.

Variational inference (VI) combined with data subsampling enables approximate posterior inference with large data sets for otherwise intractable models, but suffers from poor local optima. We first formulate a deterministic annealing approach for the generic class of conditionally conjugate exponential family models. This algorithm uses a temperature parameter that deterministically deforms the objective and reduces this parameter over the course of the optimization. A well-known drawback in annealing is the choice of the annealing schedule. We therefore introduce variational tempering, a variational algorithm that introduces a temperature latent variable to the model. In contrast to related work in the Markov chain Monte Carlo literature, this algorithm results in adaptive annealing schedules. Lastly, we develop local variational tempering, which assigns a latent temperature to each data point; this allows for dynamic annealing that varies across data. Compared to the traditional VI, all proposed approaches find improved predictive likelihoods on held-out data.

Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show that SGD with constant rates can be effectively used as an approximate posterior inference algorithm for probabilistic modeling. Specifically, we show how to adjust the tuning parameters of SGD such as to match the resulting stationary distribution to the posterior. This analysis rests on interpreting SGD as a continuous-time stochastic process and then minimizing the Kullback-Leibler divergence between its stationary distribution and the target posterior. (This is in the spirit of variational inference.) In more detail, we model SGD as a multivariate Ornstein-Uhlenbeck process and then use properties of this process to derive the optimal parameters. This theoretical framework also connects SGD to modern scalable inference algorithms; we analyze the recently proposed stochastic gradient Fisher scoring under this perspective. We demonstrate that SGD with properly chosen constant rates gives a new way to optimize hyperparameters in probabilistic models.

Word embeddings are a powerful approach to capturing semantic similarity among terms in a vocabulary. In this paper, we develop exponential family embeddings, which extends the idea of word embeddings to other types of high-dimensional data. As examples, we studied several types of data: neural data with real-valued observations, count data from a market basket analysis, and ratings data from a movie recommendation system. The main idea is that each observation is modeled conditioned on a set of latent embeddings and other observations, called the context, where the way the context is defined depends on the problem. In language the context is the surrounding words; in neuroscience the context is close-by neurons; in market basket data the context is other items in the shopping cart. Each instance of an embedding defines the context, the exponential family of conditional distributions, and how the embedding vectors are shared across data. We infer the embeddings with stochastic gradient descent, with an algorithm that connects closely to generalized linear models. On all three of our applications—neural activity of zebrafish, users’ shopping behavior, and movie ratings—we found that exponential family embedding models are more effective than other dimension reduction methods. They better reconstruct held-out data and find interesting qualitative structure.