The distribution of the weights of modern deep neural networks (DNNs) - crucial for uncertainty quantification and robustness - is an eminently complex object due to its extremely high dimensionality. This paper proposes one of the first large-scale explorations of the posterior distribution of deep Bayesian Neural Networks (BNNs), expanding its study to real-world vision tasks and architectures. Specifically, we investigate the optimal approach for approximating the posterior, analyze the connection between posterior quality and uncertainty quantification, delve into the impact of modes on the posterior, and explore methods for visualizing the posterior. Moreover, we uncover weight-space symmetries as a critical aspect for understanding the posterior. To this extent, we develop an in-depth assessment of the impact of both permutation and scaling symmetries that tend to obfuscate the Bayesian posterior. While the first type of transformation is known for duplicating modes, we explore the relationship between the latter and L2 regularization, challenging previous misconceptions. Finally, to help the community improve our understanding of the Bayesian posterior, we will shortly release the first large-scale checkpoint dataset, including thousands of real-world models and our codes.

Estimating the counterfactual outcome of treatment is essential for decision-making in public health and clinical science, among others. Often, treatments are administered in a sequential, time-varying manner, leading to an exponentially increased number of possible counterfactual outcomes. Furthermore, in modern applications, the outcomes are high-dimensional and conventional average treatment effect estimation fails to capture disparities in individuals. To tackle these challenges, we propose a novel conditional generative framework capable of producing counterfactual samples under time-varying treatment, without the need for explicit density estimation. Our method carefully addresses the distribution mismatch between the observed and counterfactual distributions via a loss function based on inverse probability weighting. We present a thorough evaluation of our method using both synthetic and real-world data. Our results demonstrate that our method is capable of generating high-quality counterfactual samples and outperforms the state-of-the-art baselines.

Markov Chain Monte Carlo methods for sampling from complex distributions and estimating normalization constants often simulate samples from a sequence of intermediate distributions along an annealing path, which bridges between a tractable initial distribution and a target density of interest. Prior work has constructed annealing paths using quasi-arithmetic means, and interpreted the resulting intermediate densities as minimizing an expected divergence to the endpoints. We provide a comprehensive analysis of this 'centroid' property using Bregman divergences under a monotonic embedding of the density function, thereby associating common divergences such as Amari's and Renyi's ${\alpha}$-divergences, ${(\alpha,\beta)}$-divergences, and the Jensen-Shannon divergence with intermediate densities along an annealing path. Our analysis highlights the interplay between parametric families, quasi-arithmetic means, and divergence functions using the rho-tau Bregman divergence framework of Zhang 2004,2013.

Understanding the power of parameterized quantum circuits (PQCs) in accomplishing machine learning tasks is one of the most important questions in quantum machine learning. In this paper, we analyze the expressivity of PQCs through the lens of function approximation. Previously established universal approximation theorems for PQCs are mainly nonconstructive, leading us to the following question: How large do the PQCs need to be to approximate the target function up to a given error? We exhibit explicit constructions of data re-uploading PQCs for approximating continuous and smooth functions and establish quantitative approximation error bounds in terms of the width, the depth and the number of trainable parameters of the PQCs. To achieve this, we utilize techniques from quantum signal processing and linear combinations of unitaries to construct PQCs that implement multivariate polynomials. We implement global and local approximation techniques using Bernstein polynomials and local Taylor expansion and analyze their performances in the quantum setting. We also compare our proposed PQCs to nearly optimal deep neural networks in approximating high-dimensional smooth functions, showing that the ratio between model sizes of PQC and deep neural networks is exponentially small with respect to the input dimension. This suggests a potentially novel avenue for showcasing quantum advantages in quantum machine learning.

Merging into dense highway traffic for an autonomous vehicle is a complex decision-making task, wherein the vehicle must identify a potential gap and coordinate with surrounding human drivers, each of whom may exhibit diverse driving behaviors. Many existing methods consider other drivers to be dynamic obstacles and, as a result, are incapable of capturing the full intent of the human drivers via this passive planning. In this paper, we propose a novel dual control framework based on Model Predictive Path-Integral control to generate interactive trajectories. This framework incorporates a Bayesian inference approach to actively learn the agents' parameters, i.e., other drivers' model parameters. The proposed framework employs a sampling-based approach that is suitable for real-time implementation through the utilization of GPUs. We illustrate the effectiveness of our proposed methodology through comprehensive numerical simulations conducted in both high and low-fidelity simulation scenarios focusing on autonomous on-ramp merging.

Designing and developing Artificial Intelligence controllers on separately dedicated chips have many advantages. This report reviews the development of a real-time fuzzy logic controller for optimizing locomotion control of a two-wheeled differential drive platform using an Arduino Uno board. Based on the Raspberry Pi board, fuzzy sets are used to optimize color recognition, enabling the color sensor to correctly recognize color at long distances, across a wide range of light intensity, and with high fault tolerance.

This paper studies the fundamental problem of learning multi-layer generator models. The multi-layer generator model builds multiple layers of latent variables as a prior model on top of the generator, which benefits learning complex data distribution and hierarchical representations. However, such a prior model usually focuses on modeling inter-layer relations between latent variables by assuming non-informative (conditional) Gaussian distributions, which can be limited in model expressivity. To tackle this issue and learn more expressive prior models, we propose an energy-based model (EBM) on the joint latent space over all layers of latent variables with the multi-layer generator as its backbone. Such joint latent space EBM prior model captures the intra-layer contextual relations at each layer through layer-wise energy terms, and latent variables across different layers are jointly corrected. We develop a joint training scheme via maximum likelihood estimation (MLE), which involves Markov Chain Monte Carlo (MCMC) sampling for both prior and posterior distributions of the latent variables from different layers. To ensure efficient inference and learning, we further propose a variational training scheme where an inference model is used to amortize the costly posterior MCMC sampling. Our experiments demonstrate that the learned model can be expressive in generating high-quality images and capturing hierarchical features for better outlier detection.

This paper presents two computationally efficient algorithms for the orientation estimation of inertial measurement units (IMUs): the correntropy-based gradient descent (CGD) and the correntropy-based decoupled orientation estimation (CDOE). Traditional methods, such as gradient descent (GD) and decoupled orientation estimation (DOE), rely on the mean squared error (MSE) criterion, making them vulnerable to external acceleration and magnetic interference. To address this issue, we demonstrate that the multi-kernel correntropy loss (MKCL) is an optimal objective function for maximum likelihood estimation (MLE) when the noise follows a type of heavy-tailed distribution. In certain situations, the estimation error of the MKCL is bounded even in the presence of arbitrarily large outliers. By replacing the standard MSE cost function with MKCL, we develop the CGD and CDOE algorithms. We evaluate the effectiveness of our proposed methods by comparing them with existing algorithms in various situations. Experimental results indicate that our proposed methods (CGD and CDOE) outperform their conventional counterparts (GD and DOE), especially when faced with external acceleration and magnetic disturbances. Furthermore, the new algorithms demonstrate significantly lower computational complexity than Kalman filter-based approaches, making them suitable for applications with low-cost microprocessors.

Goal-conditioned reinforcement learning (GCRL) refers to learning general-purpose skills that aim to reach diverse goals. In particular, offline GCRL only requires purely pre-collected datasets to perform training tasks without additional interactions with the environment. Although offline GCRL has become increasingly prevalent and many previous works have demonstrated its empirical success, the theoretical understanding of efficient offline GCRL algorithms is not well established, especially when the state space is huge and the offline dataset only covers the policy we aim to learn. In this paper, we provide a rigorous theoretical analysis of an existing empirically successful offline GCRL algorithm. We prove that under slight modification, this algorithm enjoys an $\widetilde{O}(\text{poly}(1/\epsilon))$ sample complexity (where $\epsilon$ is the desired suboptimality of the learned policy) with general function approximation thanks to the property of (semi-)strong convexity of the objective functions. We only require nearly minimal assumptions on the dataset (single-policy concentrability) and the function class (realizability). Moreover, this algorithm consists of two uninterleaved optimization steps, which we refer to as $V$-learning and policy learning, and is computationally stable since it does not involve minimax optimization. We also empirically validate our theory by showing that the modified algorithm outperforms the previous algorithm in various real-world environments. To the best of our knowledge, this is the first algorithm that is both provably efficient with general function approximation and single-policy concentrability, and empirically successful without requiring solving minimax optimization problems.

This paper provides a comprehensive survey of bias mitigation methods for achieving fairness in Machine Learning (ML) models. We collect a total of 341 publications concerning bias mitigation for ML classifiers. These methods can be distinguished based on their intervention procedure (i.e., pre-processing, in-processing, post-processing) and the technique they apply. We investigate how existing bias mitigation methods are evaluated in the literature. In particular, we consider datasets, metrics and benchmarking. Based on the gathered insights (e.g., What is the most popular fairness metric? How many datasets are used for evaluating bias mitigation methods?), we hope to support practitioners in making informed choices when developing and evaluating new bias mitigation methods.