Deep latent variable models (DLVMs) combine the approximation abilities of deep neural networks and the statistical foundations of generative models. Variational methods are commonly used for inference; however, the exact likelihood of these models has been largely overlooked. The purpose of this work is to study the general properties of this quantity and to show how they can be leveraged in practice. We focus on important inferential problems that rely on the likelihood: estimation and missing data imputation. First, we investigate maximum likelihood estimation for DLVMs: in particular, we show that most unconstrained models used for continuous data have an unbounded likelihood function. This problematic behaviour is demonstrated to be a source of mode collapse. We also show how to ensure the existence of maximum likelihood estimates, and draw useful connections with nonparametric mixture models. Finally, we describe an algorithm for missing data imputation using the exact conditional likelihood of a DLVM. On several data sets, our algorithm consistently and significantly outperforms the usual imputation scheme used for DLVMs.

Offline reinforcement learning (RL) aims to learn decision policies from a fixed batch of logged transitions, without additional environment interaction. Despite remarkable empirical progress, offline RL remains fragile under distribution shifts: value-based methods can overestimate the value of unseen actions, yielding policies that exploit model errors rather than genuine long-term rewards. We propose \emph{Bayesian Conservative Policy Optimization (BCPO)}, a unified framework that converts epistemic uncertainty into \emph{provably conservative} policy improvement. BCPO maintains a hierarchical Bayesian posterior over environment/value models, constructs a \emph{credible lower bound} (LCB) on action values, and performs policy updates under explicit KL regularization toward the behavior distribution. This yields an uncertainty-calibrated analogue of conservative policy iteration in the offline regime. We provide a finite-MDP theory showing that the pessimistic fixed point lower-bounds the true value function with high probability and that KL-controlled updates improve a computable return lower bound. Empirically, we verify the methodology on a real offline replay dataset for the CartPole benchmark obtained via the \texttt{d3rlpy} ecosystem, and report diagnostics that link uncertainty growth and policy drift to offline instability, motivating principled early stopping and calibration

Collecting multiple types of data on the same set of subjects is common in modern scientific applications including, genomics, metabolomics, and neuroimaging. Joint and Individual Variance Explained (JIVE) seeks a low-rank approximation of the joint variation between two or more sets of features captured on common subjects and isolates this variation from that unique to eachset of features. We develop an expectation-maximization (EM) algorithm to estimate a probabilistic model for the JIVE framework. The model extends probabilistic principal components analysis to multiple data sets. Our maximum likelihood approach simultaneously estimates joint and individual components, which can lead to greater accuracy compared to other methods. We apply ProJIVE to measures of brain morphometry and cognition in Alzheimer's disease. ProJIVE learns biologically meaningful courses of variation, and the joint morphometry and cognition subject scores are strongly related to more expensive existing biomarkers. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Code to reproduce the analysis is available on our GitHub page.

Random sample consensus (RANSAC), which is based on a repetitive sampling from a given dataset, is one of the most popular robust estimation methods. In this study, an energy-based model (EBM) for robust estimation that has a similar scheme to RANSAC, energy-based RANSAC (EB-RANSAC), is proposed. EB-RANSAC is applicable to a wide range of estimation problems similar to RANSAC. However, unlike RANSAC, EB-RANSAC does not require a troublesome sampling procedure and has only one hyperparameter. The effectiveness of EB-RANSAC is numerically demonstrated in two applications: a linear regression and maximum likelihood estimation.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Program synthesis of general-purpose source code from natural language specifi-cations is challenging due to the need to reason about high-level patterns in thetarget program and low-level implementation details at the same time.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/