We study the problem of off-policy evaluation (OPE) for episodic Partially Observable Markov Decision Processes (POMDPs) with continuous states. Motivated by the recently proposed proximal causal inference framework, we develop a non-parametric identification result for estimating the policy value via a sequence of so-called V-bridge functions with the help of time-dependent proxy variables. We then develop a fitted-Q-evaluation-type algorithm to estimate V-bridge functions recursively, where a non-parametric instrumental variable (NPIV) problem is solved at each step. By analyzing this challenging sequential NPIV estimation, we establish the finite-sample error bounds for estimating the V-bridge functions and accordingly that for evaluating the policy value, in terms of the sample size, length of horizon and so-called (local) measure of ill-posedness at each step. To the best of our knowledge, this is the first finite-sample error bound for OPE in POMDPs under non-parametric models.

We study Reinforcement Learning for partially observable systems using function approximation. We propose a new PO-bilinear framework, that is general enough to include models such as undercomplete tabular Partially Observable Markov Decision Processes (POMDPs), Linear Quadratic Gaussian (LQG), Predictive State Representations (PSRs), as well as a newly introduced model Hilbert Space Embeddings of POMDPs. Under this framework, we propose an actor-critic style algorithm that is capable to performing agnostic policy learning. Given a policy class that consists of memory based policies (i.e., policy that looks at a fixed-length window of recent observations), and a value function class that consists of functions taking both memory and future observations as inputs, our algorithm learns to compete against the best memory-based policy among the policy class. For certain examples such as undercomplete POMDPs and LQGs, by leveraging their special properties, our algorithm is even capable of competing against the globally optimal policy without paying an exponential dependence on the horizon.

Sampling from complex target distributions is a challenging task fundamental to Bayesian inference. Parallel tempering (PT) addresses this problem by constructing a Markov chain on the expanded state space of a sequence of distributions interpolating between the posterior distribution and a fixed reference distribution, which is typically chosen to be the prior. However, in the typical case where the prior and posterior are nearly mutually singular, PT methods are computationally prohibitive. In this work we address this challenge by constructing a generalized annealing path connecting the posterior to an adaptively tuned variational reference. The reference distribution is tuned to minimize the forward (inclusive) KL divergence to the posterior distribution using a simple, gradient-free moment-matching procedure. We show that our adaptive procedure converges to the forward KL minimizer, and that the forward KL divergence serves as a good proxy to a previously developed measure of PT performance. We also show that in the large-data limit in typical Bayesian models, the proposed method improves in performance, while traditional PT deteriorates arbitrarily. Finally, we introduce PT with two references---one fixed, one variational---with a novel split annealing path that ensures stable variational reference adaptation. The paper concludes with experiments that demonstrate the large empirical gains achieved by our method in a wide range of realistic Bayesian inference scenarios.

A persistent challenge in conditional image synthesis has been to generate diverse output images from the same input image despite only one output image being observed per input image. GAN-based methods are prone to mode collapse, which leads to low diversity. To get around this, we leverage Implicit Maximum Likelihood Estimation (IMLE) which can overcome mode collapse fundamentally. IMLE uses the same generator as GANs but trains it with a different, non-adversarial objective which ensures each observed image has a generated sample nearby. Unfortunately, to generate high-fidelity images, prior IMLE-based methods require a large number of samples, which is expensive. In this paper, we propose a new method to get around this limitation, which we dub Conditional Hierarchical IMLE (CHIMLE), which can generate high-fidelity images without requiring many samples. We show CHIMLE significantly outperforms the prior best IMLE, GAN and diffusion-based methods in terms of image fidelity and mode coverage across four tasks, namely night-to-day, 16x single image super-resolution, image colourization and image decompression. Quantitatively, our method improves Fréchet Inception Distance (FID) by 36.9% on average compared to the prior best IMLE-based method, and by 27.5% on average compared to the best non-IMLE-based general-purpose methods. More results and code are available on the project website at https://niopeng.github.io/CHIMLE/.

The predictive ability of supervised learning algorithms hinges on the quality of annotated examples, whose labels often come from multiple crowdsourced annotators with diverse expertise. To aggregate noisy crowdsourced annotations, many existing methods employ an annotator-specific instance-independent noise transition matrix to characterize the labeling skills of each annotator. Learning an instance-dependent noise transition model, however, is challenging and remains relatively less explored. To address this problem, in this paper, we formulate the noise transition model in a Bayesian framework and subsequently design a new label correction algorithm.

Establishing central limit theorems (CLTs) for ergodic averages of Markov chains is a fundamental problem in probability and its applications. Since the seminal work~\cite{MR834478}, a vast literature has emerged on the sufficient conditions for such CLTs. To counterbalance this, the present paper provides verifiable necessary conditions for CLTs of ergodic averages of Markov chains on general state spaces. Our theory is based on drift conditions, which also yield lower bounds on the rates of convergence to stationarity in various metrics. The validity of the ergodic CLT is of particular importance for sampling algorithms, where it underpins the error analysis of estimators in Bayesian statistics and machine learning. Although heavy-tailed sampling is of central importance in applications, the characterisation of the CLT and the convergence rates are theoretically poorly understood for almost all practically-used Markov chain Monte Carlo (MCMC) algorithms. In this setting our results provide sharp conditions on the validity of the ergodic CLT and establish convergence rates for large families of MCMC sampling algorithms for heavy-tailed targets. Our study includes a rather complete analyses for random walk Metropolis samplers (with finite- and infinite-variance proposals), Metropolis-adjusted and unadjusted Langevin algorithms and the stereographic projection sampler (as well as the independence sampler). By providing these sharp results via our practical drift conditions, our theory offers significant insights into the problems of algorithm selection and comparison for sampling heavy-tailed distributions (see short YouTube presentations~\cite{YouTube_talk} describing our \href{https://youtu.be/m2y7U4cEqy4}{\underline{theory}} and \href{https://youtu.be/w8I_oOweuko}{\underline{applications}}).

Standard approaches to causal inference, such as Outcome Regression and Inverse Probability Weighted Regression Adjustment (IPWRA), are typically derived through the lens of missing data imputation and identification theory. In this work, we unify these methods from a Machine Learning perspective, reframing ATE estimation as a \textit{domain adaptation problem under distribution shift}. We demonstrate that the canonical Hajek estimator is a special case of IPWRA restricted to a constant hypothesis class, and that IPWRA itself is fundamentally Importance-Weighted Empirical Risk Minimization designed to correct for the covariate shift between the treated sub-population and the target population. Leveraging this unified framework, we critically examine the optimization objectives of Doubly Robust estimators. We argue that standard methods enforce \textit{sufficient but not necessary} conditions for consistency by requiring outcome models to be individually unbiased. We define the true "ATE Risk Function" and show that minimizing it requires only that the biases of the treated and control models structurally cancel out. Exploiting this insight, we propose the \textbf{Joint Robust Estimator (JRE)}. Instead of treating propensity estimation and outcome modeling as independent stages, JRE utilizes bootstrap-based uncertainty quantification of the propensity score to train outcome models jointly. By optimizing for the expected ATE risk over the distribution of propensity scores, JRE leverages model degrees of freedom to achieve robustness against propensity misspecification. Simulation studies demonstrate that JRE achieves up to a 15\% reduction in MSE compared to standard IPWRA in finite-sample regimes with misspecified outcome models.

Sampling from multimodal distributions is a central challenge in Bayesian inference and machine learning. In light of hardness results for sampling -- classical MCMC methods, even with tempering, can suffer from exponential mixing times -- a natural question is how to leverage additional information, such as a warm start point for each mode, to enable faster mixing across modes. To address this, we introduce Reweighted ALPS (Re-ALPS), a modified version of the Annealed Leap-Point Sampler (ALPS) that dispenses with the Gaussian approximation assumption. We prove the first polynomial-time bound that works in a general setting, under a natural assumption that each component contains significant mass relative to the others when tilted towards the corresponding warm start point. Similarly to ALPS, we define distributions tilted towards a mixture centered at the warm start points, and at the coldest level, use teleportation between warm start points to enable efficient mixing across modes. In contrast to ALPS, our method does not require Hessian information at the modes, but instead estimates component partition functions via Monte Carlo. This additional estimation step is crucial in allowing the algorithm to handle target distributions with more complex geometries besides approximate Gaussian. For the proof, we show convergence results for Markov processes when only part of the stationary distribution is well-mixing and estimation for partition functions for individual components of a mixture. We numerically evaluate our algorithm's mixing performance compared to ALPS on a mixture of heavy-tailed distributions.

Given a probability distribution $μ$ in $\mathbb{R}^d$ represented by data, we study in this paper the generative modeling of its conditional probability distributions on the level-sets of a collective variable $ξ: \mathbb{R}^d \rightarrow \mathbb{R}^k$, where $1 \le k

We address network structure learning from zero-inflated count data by casting each node as a zero-inflated generalized linear model and optimizing a smooth, score-based objective under a directed acyclic graph constraint. Our Zero-Inflated Continuous Optimization (ZICO) approach uses node-wise likelihoods with canonical links and enforces acyclicity through a differentiable surrogate constraint combined with sparsity regularization. ZICO achieves superior performance with faster runtimes on simulated data. It also performs comparably to or better than common algorithms for reverse engineering gene regulatory networks. ZICO is fully vectorized and mini-batched, enabling learning on larger variable sets with practical runtimes in a wide range of domains.