Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately, the usual Bayesian computations can be quite challenging and expensive. Here we start with a recently proposed empirical Bayes solution, with strong theoretical convergence properties, and develop a novel and computationally efficient variational approximation thereof. One such novelty is that we develop this approximation directly for the marginal distribution on the model space, rather than on the regression coefficients themselves. We demonstrate the method's strong performance in simulations, and prove that our variational approximation inherits the strong selection consistency property satisfied by the posterior distribution that it is approximating.

With the strengths of both deep learning and kernel methods like Gaussian Processes (GPs), Deep Kernel Learning (DKL) has gained considerable attention in recent years. From the computational perspective, however, DKL becomes challenging when the input dimension of the GP layer is high. To address this challenge, we propose the Deep Additive Kernel (DAK) model, which incorporates i) an additive structure for the last-layer GP; and ii) induced prior approximation for each GP unit. This naturally leads to a last-layer Bayesian neural network (BNN) architecture. The proposed method enjoys the interpretability of DKL as well as the computational advantages of BNN. Empirical results show that the proposed approach outperforms state-of-the-art DKL methods in both regression and classification tasks.

The challenge arises from heteroscedasticity, which implies that the covariance is sample dependent and is often unknown. Consequently, recent methods learn the covariance through unsupervised frameworks, which unfortunately yield a trade-off between computational complexity and accuracy. While this trade-off could be alleviated through supervision, obtaining labels for the covariance is non-trivial. Here, we study self-supervised covariance estimation in deep heteroscedastic regression. We address two questions: (1) How should we supervise the covariance assuming ground truth is available? We address (1) by analysing two popular measures: the KL Divergence and the 2-Wasserstein distance. Subsequently, we derive an upper bound on the 2-Wasserstein distance between normal distributions with non-commutative covariances that is stable to optimize. We address (2) through a simple neighborhood based heuristic algorithm which results in surprisingly effective pseudo-labels for the covariance. Our experiments over a wide range of synthetic and real datasets demonstrate that the proposed 2-Wasserstein bound coupled with pseudo-label annotations results in a computationally cheaper yet accurate deep heteroscedastic regression. The target distribution is typically used for downstream tasks such as uncertainty estimation, correlation analysis, sampling, and in bayesian frameworks. The key challenge in deep heteroscedastic regression lies in estimating heteroscedasticity, which implies that the variance of the target is input dependent and variable. Moreover, unlike the mean, the covariance lacks direct supervision and needs to be inferred. The standard approach without the ground-truth covariance relies on optimizing the negative loglikelihood to jointly learn the mean and covariance (Dorta et al., 2018).

Advances in deep learning and representation learning have transformed item factor analysis (IFA) in the item response theory (IRT) literature by enabling more efficient and accurate parameter estimation. Variational Autoencoders (VAEs) have been one of the most impactful techniques in modeling high-dimensional latent variables in this context. However, the limited expressiveness of the inference model based on traditional VAEs can still hinder the estimation performance. This study introduces Adversarial Variational Bayes (AVB) algorithms as an improvement to VAEs for IFA with improved flexibility and accuracy. By bridging the strengths of VAEs and Generative Adversarial Networks (GANs), AVB incorporates an auxiliary discriminator network to reframe the estimation process as a two-player adversarial game and removes the restrictive assumption of standard normal distributions in the inference model. Theoretically, AVB can achieve similar or higher likelihood compared to VAEs. A further enhanced algorithm, Importance-weighted Adversarial Variational Bayes (IWAVB) is proposed and compared with Importance-weighted Autoencoders (IWAE). In an exploratory analysis of real empirical data, IWAVB demonstrated superior expressiveness by achieving a higher likelihood compared to IWAE. In confirmatory studies with simulated data, IWAVB achieved similar mean-square error results to IWAE while consistently achieving higher likelihoods. Moreover, in simulations where latent variables followed a multimodal distribution, IWAVB outperformed IWAE by providing more accurate parameter estimates. With its innovative use of GANs, IWAVB is shown to have the potential to extend IFA to handle large-scale data, facilitating the potential integration of psychometrics and multimodal data analysis.

This work applies modern AI tools (transformers) to solving one of the oldest statistical problems: Poisson means under empirical Bayes (Poisson-EB) setting. In Poisson-EB a high-dimensional mean vector $\theta$ (with iid coordinates sampled from an unknown prior $\pi$) is estimated on the basis of $X=\mathrm{Poisson}(\theta)$. A transformer model is pre-trained on a set of synthetically generated pairs $(X,\theta)$ and learns to do in-context learning (ICL) by adapting to unknown $\pi$. Theoretically, we show that a sufficiently wide transformer can achieve vanishing regret with respect to an oracle estimator who knows $\pi$ as dimension grows to infinity. Practically, we discover that already very small models (100k parameters) are able to outperform the best classical algorithm (non-parametric maximum likelihood, or NPMLE) both in runtime and validation loss, which we compute on out-of-distribution synthetic data as well as real-world datasets (NHL hockey, MLB baseball, BookCorpusOpen). Finally, by using linear probes, we confirm that the transformer's EB estimator appears to internally work differently from either NPMLE or Robbins' estimators.

Accurate demand forecasting is vital for ensuring reliable access to contraceptive products, supporting key processes like procurement, inventory, and distribution. However, forecasting contraceptive demand in developing countries presents challenges, including incomplete data, poor data quality, and the need to account for multiple geographical and product factors. Current methods often rely on simple forecasting techniques, which fail to capture demand uncertainties arising from these factors, warranting expert involvement. Our study aims to improve contraceptive demand forecasting by combining probabilistic forecasting methods with expert knowledge. We developed a hybrid model that combines point forecasts from domain-specific model with probabilistic distributions from statistical and machine learning approaches, enabling human input to fine-tune and enhance the system-generated forecasts. This approach helps address the uncertainties in demand and is particularly useful in resource-limited settings. We evaluate different forecasting methods, including time series, Bayesian, machine learning, and foundational time series methods alongside our new hybrid approach. By comparing these methods, we provide insights into their strengths, weaknesses, and computational requirements. Our research fills a gap in forecasting contraceptive demand and offers a practical framework that combines algorithmic and human expertise. Our proposed model can also be generalized to other humanitarian contexts with similar data patterns.

Recent work reported that simple Bayesian optimization methods perform well for high-dimensional real-world tasks, seemingly contradicting prior work and tribal knowledge. This paper investigates the 'why'. We identify fundamental challenges that arise in high-dimensional Bayesian optimization and explain why recent methods succeed. Our analysis shows that vanishing gradients caused by Gaussian process initialization schemes play a major role in the failures of high-dimensional Bayesian optimization and that methods that promote local search behaviors are better suited for the task. We find that maximum likelihood estimation of Gaussian process length scales suffices for state-of-the-art performance. Based on this, we propose a simple variant of maximum likelihood estimation called MSR that leverages these findings to achieve state-of-the-art performance on a comprehensive set of real-world applications. We also present targeted experiments to illustrate and confirm our findings.

Autonomous agents are often required to plan under multiple objectives whose preference ordering varies based on context. The agent may encounter multiple contexts during its course of operation, each imposing a distinct lexicographic ordering over the objectives, with potentially different reward functions associated with each context. Existing approaches to multi-objective planning typically consider a single preference ordering over the objectives, across the state space, and do not support planning under multiple objective orderings within an environment. We present Contextual Lexicographic Markov Decision Process (CLMDP), a framework that enables planning under varying lexicographic objective orderings, depending on the context. In a CLMDP, both the objective ordering at a state and the associated reward functions are determined by the context. We employ a Bayesian approach to infer a state-context mapping from expert trajectories. Our algorithm to solve a CLMDP first computes a policy for each objective ordering and then combines them into a single context-aware policy that is valid and cycle-free. The effectiveness of the proposed approach is evaluated in simulation and using a mobile robot.

The correct way to quantify predictive uncertainty in neural networks remains a topic of active discussion. In particular, it is unclear whether the state-of-the art entropy decomposition leads to a meaningful representation of model, or epistemic, uncertainty (EU) in the light of a debate that pits ignorance against disagreement perspectives. We aim to reconcile the conflicting viewpoints by arguing that both are valid but arise from different learning situations. Notably, we show that the presence of shortcuts is decisive for EU manifesting as disagreement.

One of the main challenges in statistics is the design of a universal estimation procedure. Given data, a universal procedure is an algorithm that provides an estimator of the generating distribution which is simultaneously statistically consistent when the true distribution belongs to the model, and robust otherwise. Typically, a universal estimator is consistent for any model, with minimaxoptimal or fast rates of convergence and is robust to small departures from the model assumptions [Bickel, 1976] such as sparse instead of dense effects or non-Gaussian errors in high dimensional linear regression. Unfortunately, most statistical procedures are based upon strong assumptions on the model or on the corresponding parameter set, and very famous estimation methods such as maximum likelihood estimation (MLE), method of moments or Bayesian posterior inference may fail even on simple problems when such assumptions do not hold. For instance, even though MLE is consistent and asymptotically normal with optimal rates of convergence in parametric estimation under suitable regularity assumptions [Le Cam, 1970, Van der Vaart, 1990] and in nonparametric estimation under entropy conditions, this method behaves poorly in case of misspecification when the true generating distribution of the data does not belong to the chosen model. Let us investigate a simple example presented in [Birgé, 2006] that illustrates the non-universal characteristic of MLE. We observe a collection of n independent and identically distributed (i.i.d) random variables X