We introduce HDP-Flow, a Bayesian nonparametric (BNP) model for unsupervised state discovery in dynamic, non-stationary time series data. Unlike prior work that assumes fixed states, HDPFlow models evolving datasets with unknown and variable latent states. By integrating the adaptability of BNP models with the expressive power of normalizing flows, HDP-Flow effectively models dynamic, non-stationary patterns, while learning transferable states across datasets with wellcalibrated uncertainty. We propose a scalable variational algorithm to enable efficient inference, addressing the limitations of traditional sampling-based BNP methods. HDP-Flow outperforms existing approaches in latent state identification and provides probabilistic insight into state distributions and transition dynamics. Evaluating HDP-Flow across two wearable datasets demonstrates transferability of states across diverse sub-populations, validating its robustness and generalizability.

Statistical model discovery is a challenging search over a vast space of models subject to domain-specific constraints. Efficiently searching over this space requires expertise in modeling and the problem domain. Motivated by the domain knowledge and programming capabilities of large language models (LMs), we introduce a method for language model driven automated statistical model discovery. We cast our automated procedure within the principled framework of Box’s Loop: the LM iterates between proposing statistical models represented as probabilistic programs, acting as a modeler, and critiquing those models, acting as a domain expert. By leveraging LMs, we do not have to define a domain-specific language of models or design a handcrafted search procedure, which are key restrictions of previous systems. We evaluate our method in three settings in probabilistic modeling: searching within a restricted space of models, searching over an open-ended space, and improving expert models under natural language constraints (e.g., this model should be interpretable to an ecologist). Our method identifies models on par with human expert designed models and extends classic models in interpretable ways. Our results highlight the promise of LM-driven model discovery.

Hybrid models composing mechanistic ODE-based dynamics with flexible and expressive neural network components have grown rapidly in popularity, especially in scientific domains where such ODE-based modeling offers important interpretability and validated causal grounding (e.g., for counterfactual reasoning). The incorporation of mechanistic models also provides inductive bias in standard blackbox modeling approaches, critical when learning from small datasets or partially observed, complex systems. Unfortunately, as the hybrid models become more flexible, the causal grounding provided by the mechanistic model can quickly be lost. We address this problem by leveraging another common source of domain knowledge: ranking of treatment effects for a set of interventions, even if the precise treatment effect is unknown. We encode this information in a causal loss that we combine with the standard predictive loss to arrive at a hybrid loss that biases our learning towards causally valid hybrid models. We demonstrate our ability to achieve a win-win, state-of-the-art predictive performance and causal validity, in the challenging task of modeling glucose dynamics post-exercise in individuals with type 1 diabetes.

Efficiently capturing the long-range patterns in sequential data sources salient to a given task---such as classification and generative modeling---poses a fundamental challenge. Popular approaches in the space tradeoff between the memory burden of brute-force enumeration and comparison, as in transformers, the computational burden of complicated sequential dependencies, as in recurrent neural networks, or the parameter burden of convolutional networks with many or large filters. We instead take inspiration from wavelet-based multiresolution analysis to define a new building block for sequence modeling, which we call a MultiresLayer. The key component of our model is the multiresolution convolution, capturing multiscale trends in the input sequence. Our MultiresConv can be implemented with shared filters across a dilated causal convolution tree. Thus it garners the computational advantages of convolutional networks and the principled theoretical motivation of wavelet decompositions. Our MultiresLayer is straightforward to implement, requires significantly fewer parameters, and maintains at most a $O(N \log N)$ memory footprint for a length $N$ sequence. Yet, by stacking such layers, our model yields state-of-the-art performance on a number of sequence classification and autoregressive density estimation tasks using CIFAR-10, ListOps, and PTB-XL datasets.

While most classical approaches to Granger causality detection assume linear dynamics, many interactions in real-world applications, like neuroscience and genomics, are inherently nonlinear. In these cases, using linear models may lead to inconsistent estimation of Granger causal interactions. We propose a class of nonlinear methods by applying structured multilayer perceptrons (MLPs) or recurrent neural networks (RNNs) combined with sparsity-inducing penalties on the weights. By encouraging specific sets of weights to be zero-in particular, through the use of convex group-lasso penalties-we can extract the Granger causal structure. To further contrast with traditional approaches, our framework naturally enables us to efficiently capture long-range dependencies between series either via our RNNs or through an automatic lag selection in the MLP. We show that our neural Granger causality methods outperform state-of-the-art nonlinear Granger causality methods on the DREAM3 challenge data. This data consists of nonlinear gene expression and regulation time courses with only a limited number of time points. The successes we show in this challenging dataset provide a powerful example of how deep learning can be useful in cases that go beyond prediction on large datasets. We likewise illustrate our methods in detecting nonlinear interactions in a human motion capture dataset.

One of the challenges in machine learning research is to ensure that presented and published results are sound and reliable. Reproducibility, that is obtaining similar results as presented in a paper or talk, using the same code and data (when available), is a necessary step to verify the reliability of research findings. Reproducibility is also an important step to promote open and accessible research, thereby allowing the scientific community to quickly integrate new findings and convert ideas to practice. Reproducibility also promotes the use of robust experimental workflows, which potentially reduce unintentional errors. In 2019, the Neural Information Processing Systems (NeurIPS) conference, the premier international conference for research in machine learning, introduced a reproducibility program, designed to improve the standards across the community for how we conduct, communicate, and evaluate machine learning research. The program contained three components: a code submission policy, a community-wide reproducibility challenge, and the inclusion of the Machine Learning Reproducibility checklist as part of the paper submission process. In this paper, we describe each of these components, how it was deployed, as well as what we were able to learn from this initiative.

Correlation filters have provided exceptional results in the field of visual object tracking in the past few years. However, these methods typically learn a single filter to be robust to many different appearance changes, which can be challenging. We propose a simple solution to this problem by utilizing an ensemble method of base trackers trained on different temporal windows of the video history. The proposed tracker, called MTCF, exhibits the following features: i) it can be trained using gradient-based convex optimization; ii) it is robust to short-term and long-term changes in visual appearance. MTCF performs on par with or outperforms state-of-the-art trackers on the OTB and the VOT benchmark datasets. We present an extensive analysis of the performance of MTCF on these benchmark datasets.

Deep generative models have recently yielded encouraging results in producing subjectively realistic samples of complex data. Far less attention has been paid to making these generative models interpretable. In many scenarios, ranging from scientific applications to finance, the observed variables have a natural grouping. It is often of interest to understand systems of interaction amongst these groups, and latent factor models (LFMs) are an attractive approach. However, traditional LFMs are limited by assuming a linear correlation structure. We present an output interpretable VAE (oi-VAE) for grouped data that models complex, nonlinear latent-to-observed relationships. We combine a structured VAE comprised of group-specific generators with a sparsity-inducing prior. We demonstrate that oi-VAE yields meaningful notions of interpretability in the analysis of motion capture and MEG data. We further show that in these situations, the regularization inherent to oi-VAE can actually lead to improved generalization and learned generative processes.

Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space the time-discretization error can dominate when we are near the boundary of the space. We demonstrate that because of this, current SGMCMC methods for the simplex struggle with sparse simplex spaces; when many of the components are close to zero. Unfortunately, many popular large-scale Bayesian models, such as network or topic models, require inference on sparse simplex spaces. To avoid the biases caused by this discretization error, we propose the stochastic Cox-Ingersoll-Ross process (SCIR), which removes all discretization error and we prove that samples from the SCIR process are asymptotically unbiased. We discuss how this idea can be extended to target other constrained spaces. Use of the SCIR process within a SGMCMC algorithm is shown to give substantially better performance for a topic model and a Dirichlet process mixture model than existing SGMCMC approaches.

Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling Bayesian inference to large datasets under an assumption of i.i.d data. We instead develop an SG-MCMC algorithm to learn the parameters of hidden Markov models (HMMs) for time-dependent data. There are two challenges to applying SG-MCMC in this setting: The latent discrete states, and needing to break dependencies when considering minibatches. We consider a marginal likelihood representation of the HMM and propose an algorithm that harnesses the inherent memory decay of the process. We demonstrate the effectiveness of our algorithm on synthetic experiments and an ion channel recording data, with runtimes significantly outperforming batch MCMC.

In theory, Bayesian nonparametric (BNP) models are well suited to streaming data scenarios due to their ability to adapt model complexity based on the amount of data observed. Unfortunately, such benefits have not been fully realized in practice; existing inference algorithms either are not applicable to streaming applications or are not extensible to nonparametric models. For the special case of Dirichlet processes, streaming inference has been considered. However, there is growing interest in more flexible BNP models, in particular building on the class of normalized random measures (NRMs). We work within this general framework and present a streaming variational inference algorithm for NRM mixture models based on assumed density filtering. Extensions to expectation propagation algorithms are possible in the batch data setting. We demonstrate the efficacy of the algorithm on clustering documents in large, streaming text corpora.

Many recent Markov chain Monte Carlo (MCMC) samplers leverage continuous dynamics to define a transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable variants that subsample the data and use stochastic gradients in place of full-data gradients in the dynamic simulations. However, such stochastic gradient MCMC samplers have lagged behind their full-data counterparts in terms of the complexity of dynamics considered since proving convergence in the presence of the stochastic gradient noise is non-trivial. Even with simple dynamics, significant physical intuition is often required to modify the dynamical system to account for the stochastic gradient noise. In this paper, we provide a general recipe for constructing MCMC samplers--including stochastic gradient versions--based on continuous Markov processes specified via two matrices. We constructively prove that the framework is complete. That is, any continuous Markov process that provides samples from the target distribution can be written in our framework. We show how previous continuous-dynamic samplers can be trivially reinvented in our framework, avoiding the complicated sampler-specific proofs. We likewise use our recipe to straightforwardly propose a new state-adaptive sampler: stochastic gradient Riemann Hamiltonian Monte Carlo (SGRHMC). Our experiments on simulated data and a streaming Wikipedia analysis demonstrate that the proposed SGRHMC sampler inherits the benefits of Riemann HMC, with the scalability of stochastic gradient methods.

The articles in this special issue discuss the applications supported by Bayesian nonparametric modeling. These probabilistic models defined over infinite-dimensional parameter spaces. For Gaussian process models of regression and classification functions, the parameter space consists of a set of continuous functions. For the Dirichlet process mixture models used in density estimation and clustering, the parameter space is dense in the space of probability measures. Bayesian nonparametric models provide a flexible framework for modeling complex data and a promising alternative to classical model selection methods. Due to recent computational advances, these approaches have received increasing attention in machine learning, statistics, probability, and related application domains.

Determinantal point processes (DPPs) are well-suited for modeling repulsion and have proven useful in applications where diversity is desired. While DPPs have many appealing properties, learning the parameters of a DPP is difficult, as the likelihood is non-convex and is infeasible to compute in many scenarios. Here we propose Bayesian methods for learning the DPP kernel parameters. These methods are applicable in large-scale discrete and continuous DPP settings, even when the likelihood can only be bounded. We demonstrate the utility of our DPP learning methods in studying the progression of diabetic neuropathy based on the spatial distribution of nerve fibers, and in studying human perception of diversity in images.

Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard random-walk proposals. The popularity of such methods has grown significantly in recent years. However, a limitation of HMC methods is the required gradient computation for simulation of the Hamiltonian dynamical system-such computation is infeasible in problems involving a large sample size or streaming data. Instead, we must rely on a noisy gradient estimate computed from a subset of the data. In this paper, we explore the properties of such a stochastic gradient HMC approach. Surprisingly, the natural implementation of the stochastic approximation can be arbitrarily bad. To address this problem we introduce a variant that uses second-order Langevin dynamics with a friction term that counteracts the effects of the noisy gradient, maintaining the desired target distribution as the invariant distribution. Results on simulated data validate our theory. We also provide an application of our methods to a classification task using neural networks and to online Bayesian matrix factorization.

Patients with epilepsy can manifest short, sub-clinical epileptic “bursts” in addition to full-blown clinical seizures. We believe the relationship between these two classes of events—something not previously studied quantitatively—could yield important insights into the nature and intrinsic dynamics of seizures. A goal of our work is to parse these complex epileptic events into distinct dynamic regimes. A challenge posed by the intracranial EEG (iEEG) data we study is the fact that the number and placement of electrodes can vary between patients. We develop a Bayesian nonparametric Markov switching process that allows for (i) shared dynamic regimes between a variable numbers of channels, (ii) asynchronous regime-switching, and (iii) an unknown dictionary of dynamic regimes. We encode a sparse and changing set of dependencies between the channels using a Markov-switching Gaussian graphical model for the innovations process driving the channel dynamics. We demonstrate the importance of this model in parsing and out-of-sample predictions of iEEG data. We show that our model produces intuitive state assignments that can help automate clinical analysis of seizures and enable the comparison of sub-clinical bursts and full clinical seizures.

From Twitter to Facebook to Reddit, users have become accustomed to sharing the articles they read with friends or followers on their social networks. While previous work has modeled what these shared stories say about the user who shares them, the converse question remains unexplored: what can we learn about an article from the identities of its likely readers? To address this question, we model the content of news articles and blog posts by attributes of the people who are likely to share them. For example, many Twitter users describe themselves in a short profile, labeling themselves with phrases such as "vegetarian" or "liberal." By assuming that a user's labels correspond to topics in the articles he shares, we can learn a labeled dictionary from a training corpus of articles shared on Twitter. Thereafter, we can code any new document as a sparse non-negative linear combination of user labels, where we encourage correlated labels to appear together in the output via a structured sparsity penalty.

Determinantal point processes (DPPs) are random point processes well-suited for modeling repulsion. In machine learning, the focus of DPP-based models has been on diverse subset selection from a discrete and finite base set. This discrete setting admits an efficient algorithm for sampling based on the eigendecomposition of the defining kernel matrix. Recently, there has been growing interest in using DPPs defined on continuous spaces. While the discrete-DPP sampler extends formally to the continuous case, computationally, the steps required cannot be directly extended except in a few restricted cases. In this paper, we present efficient approximate DPP sampling schemes based on Nystrom and random Fourier feature approximations that apply to a wide range of kernel functions. We demonstrate the utility of continuous DPPs in repulsive mixture modeling applications and synthesizing human poses spanning activity spaces.

We propose a multiresolution Gaussian process to capture long-range, non-Markovian dependencies while allowing for abrupt changes. The multiresolution GP hierarchically couples a collection of smooth GPs, each defined over an element of a random nested partition. Long-range dependencies are captured by the top-level GP while the partition points define the abrupt changes. Due to the inherent conjugacy of the GPs, one can analytically marginalize the GPs and compute the conditional likelihood of the observations given the partition tree. This allows for efficient inference of the partition itself, for which we employ graph-theoretic techniques. We apply the multiresolution GP to the analysis of Magnetoencephalography (MEG) recordings of brain activity.

Applications of Bayesian nonparametric methods require learning and inference algorithms which efficiently explore models of unbounded complexity. We develop new Markov chain Monte Carlo methods for the beta process hidden Markov model (BP-HMM), enabling discovery of shared activity patterns in large video and motion capture databases. By introducing split-merge moves based on sequential allocation, we allow large global changes in the shared feature structure. We also develop data-driven reversible jump moves which more reliably discover rare or unique behaviors. Our proposals apply to any choice of conjugate likelihood for observed data, and we show success with multinomial, Gaussian, and autoregressive emission models. Together, these innovations allow tractable analysis of hundreds of time series, where previous inference required clever initialization and at least ten thousand burn-in iterations for just six sequences.

We propose a Bayesian nonparametric approach to relating multiple time series via a set of latent, dynamical behaviors. Using a beta process prior, we allow data-driven selection of the size of this set, as well as the pattern with which behaviors are shared among time series. Via the Indian buffet process representation of the beta process predictive distributions, we develop an exact Markov chain Monte Carlo inference method. In particular, our approach uses the sum-product algorithm to efficiently compute Metropolis-Hastings acceptance probabilities, and explores new dynamical behaviors via birth/death proposals. We validate our sampling algorithm using several synthetic datasets, and also demonstrate promising unsupervised segmentation of visual motion capture data.

The hierarchical Dirichlet process hidden Markov model (HDP-HMM) is a flexible, nonparametric model which allows state spaces of unknown size to be learned from data. We demonstrate some limitations of the original HDP-HMM formulation (Teh et al., 2006), and propose a sticky extension which allows more robust learning of smoothly varying dynamics. Using DP mixtures, this formulation also allows learning of more complex, multimodal emission distributions. We further develop a sampling algorithm that employs a truncated approximation of the DP to jointly resample the full state sequence, greatly improving mixing rates. Via extensive experiments with synthetic data and the NIST speaker diarization database, we demonstrate the advantages of our sticky extension, and the utility of the HDP-HMM in real-world applications.

Many nonlinear dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. In this paper, we present a nonparametric approach to the learning of an unknown number of persistent, smooth dynamical modes by utilizing a hierarchical Dirichlet process prior. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with an efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, and the IBOVESPA stock index.

We consider the problem of state estimation for a dynamic system driven by unobserved, correlated inputs. We model these inputs via an uncertain set of temporally correlated dynamic models, where this uncertainty includes the number of modes, their associated statistics, and the rate of mode transitions. The dynamic system is formulated via two interacting graphs: a hidden Markov model (HMM) and a linear-Gaussian state space model. The HMM's state space indexes system modes, while its outputs are the unobserved inputs to the linear dynamical system. This Markovian structure accounts for temporal persistence of input regimes, but avoids rigid assumptions about their detailed dynamics. Via a hierarchical Dirichlet process (HDP) prior, the complexity of our infinite state space robustly adapts to new observations. We present a learning algorithm and computational results that demonstrate the utility of the HDP for tracking, and show that it efficiently learns typical dynamics from noisy data.

We consider the problem of detecting and localizing a material release utilizing sparse sensor measurements. We formulate the problem as one of abrupt change detection. The problem is challenging because of the sparse sensor deployment and complex system dynamics. We restrict ourselves to propagation models consisting of diffusion plus transport according to a Gaussian puff model. We derive optimal inference algorithms, provided the model parametrization is known precisely, within a hybrid detection-localization hypothesis testing framework with linear growth in the hypothesis space. The primary assumptions are that the mean wind field is deterministically known and that the Gaussian puff model is valid. Under these assumptions, we characterize the change in performance of detection, time-to-detection and localization as a function of the number of sensors. We then examine some performance impacts when the underlying dynamical model deviates from the assumed model