We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection-diffusion equation. We provide a new information theoretic perspective for understanding the ERG through the intermediary of Bayesian Statistical Inference. This connection is facilitated by the Dynamical Bayesian Inference scheme, which encodes Bayesian inference in the form of a one parameter family of probability distributions solving an integro-differential equation derived from Bayes' law. In this note, we demonstrate how the Dynamical Bayesian Inference equation is, itself, equivalent to a diffusion equation which we dub Bayesian Diffusion. Identifying the features that define Bayesian Diffusion, and mapping them onto the features that define the ERG, we obtain a dictionary outlining how renormalization can be understood as the inverse of statistical inference.

Before the transition of AVs to urban roads and subsequently unprecedented changes in traffic conditions, evaluation of transportation policies and futuristic road design related to pedestrian crossing behavior is of vital importance. Recent studies analyzed the non-causal impact of various variables on pedestrian waiting time in the presence of AVs. However, we mainly investigate the causal effect of traffic density on pedestrian waiting time. We develop a Double/Debiased Machine Learning (DML) model in which the impact of confounders variable influencing both a policy and an outcome of interest is addressed, resulting in unbiased policy evaluation. Furthermore, we try to analyze the effect of traffic density by developing a copula-based joint model of two main components of pedestrian crossing behavior, pedestrian stress level and waiting time. The copula approach has been widely used in the literature, for addressing self-selection problems, which can be classified as a causality analysis in travel behavior modeling. The results obtained from copula approach and DML are compared based on the effect of traffic density. In DML model structure, the standard error term of density parameter is lower than copula approach and the confidence interval is considerably more reliable. In addition, despite the similar sign of effect, the copula approach estimates the effect of traffic density lower than DML, due to the spurious effect of confounders. In short, the DML model structure can flexibly adjust the impact of confounders by using machine learning algorithms and is more reliable for planning future policies.

Recovering underlying Directed Acyclic Graph (DAG) structures from observational data is highly challenging due to the combinatorial nature of the DAG-constrained optimization problem. Recently, DAG learning has been cast as a continuous optimization problem by characterizing the DAG constraint as a smooth equality one, generally based on polynomials over adjacency matrices. Existing methods place very small coefficients on high-order polynomial terms for stabilization, since they argue that large coefficients on the higher-order terms are harmful due to numeric exploding. On the contrary, we discover that large coefficients on higher-order terms are beneficial for DAG learning, when the spectral radiuses of the adjacency matrices are small, and that larger coefficients for higher-order terms can approximate the DAG constraints much better than the small counterparts. Based on this, we propose a novel DAG learning method with efficient truncated matrix power iteration to approximate geometric series based DAG constraints. Empirically, our DAG learning method outperforms the previous state-of-the-arts in various settings, often by a factor of $3$ or more in terms of structural Hamming distance.

The use of counterfactual explanations (CFXs) is an increasingly popular explanation strategy for machine learning models. However, recent studies have shown that these explanations may not be robust to changes in the underlying model (e.g., following retraining), which raises questions about their reliability in real-world applications. Existing attempts towards solving this problem are heuristic, and the robustness to model changes of the resulting CFXs is evaluated with only a small number of retrained models, failing to provide exhaustive guarantees. To remedy this, we propose {\Delta}-robustness, the first notion to formally and deterministically assess the robustness (to model changes) of CFXs for neural networks. We introduce an abstraction framework based on interval neural networks to verify the {\Delta}-robustness of CFXs against a possibly infinite set of changes to the model parameters, i.e., weights and biases. We then demonstrate the utility of this approach in two distinct ways. First, we analyse the {\Delta}-robustness of a number of CFX generation methods from the literature and show that they unanimously host significant deficiencies in this regard. Second, we demonstrate how embedding {\Delta}-robustness within existing methods can provide CFXs which are provably robust.

In combinatorial causal bandits (CCB), the learning agent chooses at most $K$ variables in each round to intervene, collects feedback from the observed variables, with the goal of minimizing expected regret on the target variable $Y$. We study under the context of binary generalized linear models (BGLMs) with a succinct parametric representation of the causal models. We present the algorithm BGLM-OFU for Markovian BGLMs (i.e. no hidden variables) based on the maximum likelihood estimation method, and show that it achieves $O(\sqrt{T}\log T)$ regret, where $T$ is the time horizon. For the special case of linear models with hidden variables, we apply causal inference techniques such as the do-calculus to convert the original model into a Markovian model, and then show that our BGLM-OFU algorithm and another algorithm based on the linear regression both solve such linear models with hidden variables. Our novelty includes (a) considering the combinatorial intervention action space and the general causal models including ones with hidden variables, (b) integrating and adapting techniques from diverse studies such as generalized linear bandits and online influence maximization, and (c) avoiding unrealistic assumptions (such as knowing the joint distribution of the parents of $Y$ under all interventions) and regret factors exponential to causal graph size in prior studies.

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Generative networks are opening new avenues in fast event generation for the LHC. We show how generative flow networks can reach percent-level precision for kinematic distributions, how they can be trained jointly with a discriminator, and how this discriminator improves the generation. Our joint training relies on a novel coupling of the two networks which does not require a Nash equilibrium. We then estimate the generation uncertainties through a Bayesian network setup and through conditional data augmentation, while the discriminator ensures that there are no systematic inconsistencies compared to the training data.

With advanced imaging, sequencing, and profiling technologies, multiple omics data become increasingly available and hold promises for many healthcare applications such as cancer diagnosis and treatment. Multimodal learning for integrative multi-omics analysis can help researchers and practitioners gain deep insights into human diseases and improve clinical decisions. However, several challenges are hindering the development in this area, including the availability of easily accessible open-source tools. This survey aims to provide an up-to-date overview of the data challenges, fusion approaches, datasets, and software tools from several new perspectives. We identify and investigate various omics data challenges that can help us understand the field better. We categorize fusion approaches comprehensively to cover existing methods in this area. We collect existing open-source tools to facilitate their broader utilization and development. We explore a broad range of omics data modalities and a list of accessible datasets. Finally, we summarize future directions that can potentially address existing gaps and answer the pressing need to advance multimodal learning for multi-omics data analysis.

We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. We develop approaches for learning nonlinear state space models of the dynamics for general manifold latent spaces using training strategies related to Variational Autoencoders (VAEs). Our methods are referred to as Geometric Dynamic (GD) Variational Autoencoders (GD-VAEs). We learn encoders and decoders for the system states and evolution based on deep neural network architectures that include general Multilayer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), and Transpose CNNs (T-CNNs). Motivated by problems arising in parameterized PDEs and physics, we investigate the performance of our methods on tasks for learning low dimensional representations of the nonlinear Burgers equations, constrained mechanical systems, and spatial fields of reaction-diffusion systems. GD-VAEs provide methods for obtaining representations for use in diverse learning tasks involving dynamics.

We consider the problem of dynamic pricing of a product in the presence of feature-dependent price sensitivity. Developing practical algorithms that can estimate price elasticities robustly, especially when information about no purchases (losses) is not available, to drive such automated pricing systems is a challenge faced by many industries. Based on the Poisson semi-parametric approach, we construct a flexible yet interpretable demand model where the price related part is parametric while the remaining (nuisance) part of the model is non-parametric and can be modeled via sophisticated machine learning (ML) techniques. The estimation of price-sensitivity parameters of this model via direct one-stage regression techniques may lead to biased estimates due to regularization. To address this concern, we propose a two-stage estimation methodology which makes the estimation of the price-sensitivity parameters robust to biases in the estimators of the nuisance parameters of the model. In the first-stage we construct estimators of observed purchases and prices given the feature vector using sophisticated ML estimators such as deep neural networks. Utilizing the estimators from the first-stage, in the second-stage we leverage a Bayesian dynamic generalized linear model to estimate the price-sensitivity parameters. We test the performance of the proposed estimation schemes on simulated and real sales transaction data from the Airline industry. Our numerical studies demonstrate that our proposed two-stage approach reduces the estimation error in price-sensitivity parameters from 25\% to 4\% in realistic simulation settings. The two-stage estimation techniques proposed in this work allows practitioners to leverage modern ML techniques to robustly estimate price-sensitivities while still maintaining interpretability and allowing ease of validation of its various constituent parts.