Covariates provide valuable information on external factors that influence time series and are critical in many real-world time series forecasting tasks. For example, in retail, covariates may indicate promotions or peak dates such as holiday seasons that heavily influence demand forecasts. Recent advances in pretraining large language model architectures for time series forecasting have led to highly accurate forecasters. However, the majority of these models do not readily use covariates as they are often specific to a certain task or domain. This paper introduces a new method to incorporate covariates into pretrained time series forecasting models. Our proposed approach incorporates covariate information into pretrained forecasting models through modular blocks that inject past and future covariate information, without necessarily modifying the pretrained model in consideration. In order to evaluate our approach, we introduce a benchmark composed of 32 different synthetic datasets with varying dynamics to evaluate the effectivity of forecasting models with covariates. Extensive evaluations on both synthetic and real datasets show that our approach effectively incorporates covariate information into pretrained models, outperforming existing baselines.

Generative models that satisfy hard constraints are critical in many scientific and engineering applications, where physical laws or system requirements must be strictly respected. Many existing constrained generative models, especially those developed for computer vision, rely heavily on gradient information, which is often sparse or computationally expensive in some fields, e.g., partial differential equations (PDEs). In this work, we introduce a novel framework for adapting pre-trained, unconstrained flow-matching models to satisfy constraints exactly in a zero-shot manner without requiring expensive gradient computations or fine-tuning. Our framework, *ECI sampling*, alternates between extrapolation (E), correction (C), and interpolation (I) stages during each iterative sampling step of flow matching sampling to ensure accurate integration of constraint information while preserving the validity of the generation. We demonstrate the effectiveness of our approach across various PDE systems, showing that ECI-guided generation strictly adheres to physical constraints and accurately captures complex distribution shifts induced by these constraints. Empirical results demonstrate that our framework consistently outperforms baseline approaches in various zero-shot constrained generation tasks and also achieves competitive results in the regression tasks without additional fine-tuning.

How to best develop foundational models for time series forecasting remains an important open question. Tokenization is a crucial consideration in this effort: what is an effective discrete vocabulary for a real-valued sequential input? To address this question, we develop WaveToken, a wavelet-based tokenizer that allows models to learn complex representations directly in the space of time-localized frequencies. Our method first scales and decomposes the input time series, then thresholds and quantizes the wavelet coefficients, and finally pre-trains an autoregressive model to forecast coefficients for the forecast horizon. By decomposing coarse and fine structures in the inputs, wavelets provide an eloquent and compact language for time series forecasting that simplifies learning. Empirical results on a comprehensive benchmark, including 42 datasets for both in-domain and zero-shot settings, show that WaveToken: i) performs on par or better than recently proposed foundation models for forecasting while using a much smaller vocabulary (1024 tokens), and is competitive with modern deep learning models trained specifically on each dataset; ii) exhibits superior generalization capabilities, achieving the best average rank across all datasets for three complementary metrics; and iii) easily captures complex temporal patterns of practical relevance that are challenging for other recent pre-trained models, including trends, sparse spikes, and non-stationary time series with varying frequencies evolving over time.

Since the seminal work of TabPFN, research on tabular foundation models (TFMs) based on in-context learning (ICL) has challenged long-standing paradigms in machine learning. Without seeing any real-world data, models pretrained on purely synthetic datasets generalize remarkably well across diverse datasets, often using only a moderate number of in-context examples. This shifts the focus in tabular machine learning from model architecture design to the design of synthetic datasets, or, more precisely, to the prior distributions that generate them. Yet the guiding principles for prior design remain poorly understood. This work marks the first attempt to address the gap. We systematically investigate and identify key properties of synthetic priors that allow pretrained TFMs to generalize well. Based on these insights, we introduce Mitra, a TFM trained on a curated mixture of synthetic priors selected for their diversity, distinctiveness, and performance on real-world tabular data. Mitra consistently outperforms state-of-the-art TFMs, such as TabPFNv2 and TabICL, across both classification and regression benchmarks, with better sample efficiency.

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally-trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (*predict*). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (*refine*). Notably, the generative performance of the model remains intact — downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (*synthesize*). Our code is available at https://github.com/amazon-science/unconditional-time-series-diffusion

Many complex time series can be effectively subdivided into distinct regimes that exhibit persistent dynamics. Discovering the switching behavior and the statistical patterns in these regimes is important for understanding the underlying dynamical system. We propose the Recurrent Explicit Duration Switching Dynamical System (RED-SDS), a flexible model that is capable of identifying both state- and time-dependent switching dynamics. State-dependent switching is enabled by a recurrent state-to-switch connection and an explicit duration count variable is used to improve the time-dependent switching behavior. We demonstrate how to perform efficient inference using a hybrid algorithm that approximates the posterior of the continuous states via an inference network and performs exact inference for the discrete switches and counts. The model is trained by maximizing a Monte Carlo lower bound of the marginal log-likelihood that can be computed efficiently as a byproduct of the inference routine. Empirical results on multiple datasets demonstrate that RED-SDS achieves considerable improvement in time series segmentation and competitive forecasting performance against the state of the art.

Implicit Generative Models (IGMs) such as GANs have emerged as effective data-driven models for generating samples, particularly images. In this paper, we formulate the problem of learning an IGM as minimizing the expected distance between characteristic functions. Specifically, we minimize the distance between characteristic functions of the real and generated data distributions under a suitably-chosen weighting distribution. This distance metric, which we term as the characteristic function distance (CFD), can be (approximately) computed with linear time-complexity in the number of samples, in contrast with the quadratic-time Maximum Mean Discrepancy (MMD). By replacing the discrepancy measure in the critic of a GAN with the CFD, we obtain a model that is simple to implement and stable to train. The proposed metric enjoys desirable theoretical properties including continuity and differentiability with respect to generator parameters, and continuity in the weak topology. We further propose a variation of the CFD in which the weighting distribution parameters are also optimized during training; this obviates the need for manual tuning, and leads to an improvement in test power relative to CFD. We demonstrate experimentally that our proposed method outperforms WGAN and MMD-GAN variants on a variety of unsupervised image generation benchmarks.

We address the problem of unsupervised disentanglement of latent representations learnt via deep generative models. In contrast to current approaches that operate on the evidence lower bound (ELBO), we argue that statistical independence in the latent space of VAEs can be enforced in a principled hierarchical Bayesian manner. To this effect, we augment the standard VAE with an inverse-Wishart (IW) prior on the covariance matrix of the latent code. By tuning the IW parameters, we are able to encourage (or discourage) independence in the learnt latent dimensions. Extensive experimental results on a range of datasets (2DShapes, 3DChairs, 3DFaces and CelebA) show our approach to outperform the β-VAE and is competitive with the state-of-the-art FactorVAE. Our approach achieves significantly better disentanglement and reconstruction on a new dataset (CorrelatedEllipses) which introduces correlations between the factors of variation.