The logit transform is arguably the most widely-employed link function beyond linear settings. This transformation routinely appears in regression models for binary data and provides, either explicitly or implicitly, a core building-block within state-of-the-art methodologies for both classification and regression. Its widespread use, combined with the lack of analytical solutions for the optimization of general losses involving the logit transform, still motivates active research in computational statistics. Among the directions explored, a central one has focused on the design of tangent lower bounds for logistic log-likelihoods that can be tractably optimized, while providing a tight approximation of these log-likelihoods. Although progress along these lines has led to the development of effective minorize-maximize (MM) algorithms for point estimation and coordinate ascent variational inference schemes for approximate Bayesian inference under several logit models, the overarching focus in the literature has been on tangent quadratic minorizers. In fact, it is still unclear whether tangent lower bounds sharper than quadratic ones can be derived without undermining the tractability of the resulting minorizer. This article addresses such a challenging question through the design and study of a novel piece-wise quadratic lower bound that uniformly improves any tangent quadratic minorizer, including the sharpest ones, while admitting a direct interpretation in terms of the classical generalized lasso problem. As illustrated in a ridge logistic regression, this unique connection facilitates more effective implementations than those provided by available piece-wise bounds, while improving the convergence speed of quadratic ones.

The vector quantization is a widely used method to map continuous representation to discrete space and has important application in tokenization for generative mode, bottlenecking information and many other tasks in machine learning. Vector Quantized Variational Autoencoder (VQ-VAE) is a type of variational autoencoder using discrete embedding as latent. We generalize the technique further, enriching the probabilistic framework with a Gaussian mixture as the underlying generative model. This framework leverages a codebook of latent means and adaptive variances to capture complex data distributions. This principled framework avoids various heuristics and strong assumptions that are needed with the VQ-VAE to address training instability and to improve codebook utilization. This approach integrates the benefits of both discrete and continuous representations within a variational Bayesian framework. Furthermore, by introducing the \textit{Aggregated Categorical Posterior Evidence Lower Bound} (ALBO), we offer a principled alternative optimization objective that aligns variational distributions with the generative model. Our experiments demonstrate that GM-VQ improves codebook utilization and reduces information loss without relying on handcrafted heuristics.

In this work, we have developed a variational Bayesian inference theory of elasticity, which is accomplished by using a mixed Variational Bayesian inference Finite Element Method (VBI-FEM) that can be used to solve the inverse deformation problems of continua. In the proposed variational Bayesian inference theory of continuum mechanics, the elastic strain energy is used as a prior in a Bayesian inference network, which can intelligently recover the detailed continuum deformation mappings with only given the information on the deformed and undeformed continuum body shapes without knowing the interior deformation and the precise actual boundary conditions, both traction as well as displacement boundary conditions, and the actual material constitutive relation. Moreover, we have implemented the related finite element formulation in a computational probabilistic mechanics framework. To numerically solve mixed variational problem, we developed an operator splitting or staggered algorithm that consists of the finite element (FE) step and the Bayesian learning (BL) step as an analogue of the well-known the Expectation-Maximization (EM) algorithm. By solving the mixed probabilistic Galerkin variational problem, we demonstrated that the proposed method is able to inversely predict continuum deformation mappings with strong discontinuity or fracture without knowing the external load conditions. The proposed method provides a robust machine intelligent solution for the long-sought-after inverse problem solution, which has been a major challenge in structure failure forensic pattern analysis in past several decades. The proposed method may become a promising artificial intelligence-based inverse method for solving general partial differential equations.

Within one decade, Deep Learning overtook the dominating solution methods of countless problems of artificial intelligence. ``Deep'' refers to the deep architectures with operations in manifolds of which there are no immediate observations. For these deep architectures some kind of structure is pre-defined -- but what is this structure? With a formal definition for structures of neural networks, neural architecture search problems and solution methods can be formulated under a common framework. Both practical and theoretical questions arise from closing the gap between applied neural architecture search and learning theory. Does structure make a difference or can it be chosen arbitrarily? This work is concerned with deep structures of artificial neural networks and examines automatic construction methods under empirical principles to shed light on to the so called ``black-box models''. Our contributions include a formulation of graph-induced neural networks that is used to pose optimisation problems for neural architecture. We analyse structural properties for different neural network objectives such as correctness, robustness or energy consumption and discuss how structure affects them. Selected automation methods for neural architecture optimisation problems are discussed and empirically analysed. With the insights gained from formalising graph-induced neural networks, analysing structural properties and comparing the applicability of neural architecture search methods qualitatively and quantitatively we advance these methods in two ways. First, new predictive models are presented for replacing computationally expensive evaluation schemes, and second, new generative models for informed sampling during neural architecture search are analysed and discussed.

Predicting the change in binding free energy ($\Delta \Delta G$) is crucial for understanding and modulating protein-protein interactions, which are critical in drug design. Due to the scarcity of experimental $\Delta \Delta G$ data, existing methods focus on pre-training, while neglecting the importance of alignment. In this work, we propose the Boltzmann Alignment technique to transfer knowledge from pre-trained inverse folding models to $\Delta \Delta G$ prediction. We begin by analyzing the thermodynamic definition of $\Delta \Delta G$ and introducing the Boltzmann distribution to connect energy with protein conformational distribution. However, the protein conformational distribution is intractable; therefore, we employ Bayes' theorem to circumvent direct estimation and instead utilize the log-likelihood provided by protein inverse folding models for $\Delta \Delta G$ estimation. Compared to previous inverse folding-based methods, our method explicitly accounts for the unbound state of protein complex in the $\Delta \Delta G$ thermodynamic cycle, introducing a physical inductive bias and achieving both supervised and unsupervised state-of-the-art (SoTA) performance. Experimental results on SKEMPI v2 indicate that our method achieves Spearman coefficients of 0.3201 (unsupervised) and 0.5134 (supervised), significantly surpassing the previously reported SoTA values of 0.2632 and 0.4324, respectively. Futhermore, we demonstrate the capability of our method on binding energy prediction, protein-protein docking and antibody optimization tasks.

In today's day and age where information is rapidly spread through online platforms, the rise of fake news poses an alarming threat to the integrity of public discourse, societal trust, and reputed news sources. Classical machine learning and Transformer-based models have been extensively studied for the task of fake news detection, however they are hampered by their reliance on training data and are unable to generalize on unseen headlines. To address these challenges, we propose our novel solution, leveraging web-scraping techniques and Natural Language Inference (NLI) models to retrieve external knowledge necessary for verifying the accuracy of a headline. Our system is evaluated on a diverse self-curated evaluation dataset spanning over multiple news channels and broad domains. Our best performing pipeline achieves an accuracy of 84.3% surpassing the best classical Machine Learning model by 33.3% and Bidirectional Encoder Representations from Transformers (BERT) by 31.0% . This highlights the efficacy of combining dynamic web-scraping with Natural Language Inference to find support for a claimed headline in the corresponding externally retrieved knowledge for the task of fake news detection.

Electronic commerce, or e-commerce, is the buying and selling of goods and services, or the transmitting of funds or data online. E-commerce platforms come in many kinds, with global players such as Amazon, Airbnb, Alibaba, eBay and platforms targeting specific geographic regions. Information retrieval has a natural role to play in e-commerce, especially in connecting people to goods and services. Information discovery in e-commerce concerns different types of search (e.g., exploratory search vs. lookup tasks), recommender systems, and natural language processing in e-commerce portals. The rise in popularity of e-commerce sites has made research on information discovery in e-commerce an increasingly active research area. This is witnessed by an increase in publications and dedicated workshops in this space. Methods for information discovery in e-commerce largely focus on improving the effectiveness of e-commerce search and recommender systems, on enriching and using knowledge graphs to support e-commerce, and on developing innovative question answering and bot-based solutions that help to connect people to goods and services. In this survey, an overview is given of the fundamental infrastructure, algorithms, and technical solutions for information discovery in e-commerce. The topics covered include user behavior and profiling, search, recommendation, and language technology in e-commerce.

Although existing variational graph autoencoders (VGAEs) have been widely used for modeling and generating graph-structured data, most of them are still not flexible enough to approximate the sparse and skewed latent node representations, especially those of document relational networks (DRNs) with discrete observations. To analyze a collection of interconnected documents, a typical branch of Bayesian models, specifically relational topic models (RTMs), has proven their efficacy in describing both link structures and document contents of DRNs, which motives us to incorporate RTMs with existing VGAEs to alleviate their potential issues when modeling the generation of DRNs. In this paper, moving beyond the sophisticated approximate assumptions of traditional RTMs, we develop a graph Poisson factor analysis (GPFA), which provides analytic conditional posteriors to improve the inference accuracy, and extend GPFA to a multi-stochastic-layer version named graph Poisson gamma belief network (GPGBN) to capture the hierarchical document relationships at multiple semantic levels. Then, taking GPGBN as the decoder, we combine it with various Weibull-based graph inference networks, resulting in two variants of Weibull graph auto-encoder (WGAE), equipped with model inference algorithms. Experimental results demonstrate that our models can extract high-quality hierarchical latent document representations and achieve promising performance on various graph analytic tasks.

Exact multi-label classification is the task of assigning each datapoint a set of class labels such that the assigned set exactly matches the ground truth. Optimizing for exact multi-label classification is important in domains where missing a single label can be especially costly, such as in object detection for autonomous vehicles or symptom classification for disease diagnosis. Recurrent Classifier Chains (RCCs), a recurrent neural network extension of ensemble-based classifier chains, are the state-of-the-art exact multi-label classification method for maximizing subset accuracy. However, RCCs iteratively predict classes with an unprincipled ordering, and therefore indiscriminately condition class probabilities. These disadvantages make RCCs prone to predicting inaccurate label sets. In this work we propose Recurrent Bayesian Classifier Chains (RBCCs), which learn a Bayesian network of class dependencies and leverage this network in order to condition the prediction of child nodes only on their parents.

This paper considers the challenging tasks of Multi-Agent Reinforcement Learning (MARL) under partial observability, where each agent only sees her own individual observations and actions that reveal incomplete information about the underlying state of system. This paper studies these tasks under the general model of multiplayer general-sum Partially Observable Markov Games (POMGs), which is significantly larger than the standard model of Imperfect Information Extensive-Form Games (IIEFGs). We identify a rich subclass of POMGs---weakly revealing POMGs---in which sample-efficient learning is tractable. In the self-play setting, we prove that a simple algorithm combining optimism and Maximum Likelihood Estimation (MLE) is sufficient to find approximate Nash equilibria, correlated equilibria, as well as coarse correlated equilibria of weakly revealing POMGs, in a polynomial number of samples when the number of agents is small. In the setting of playing against adversarial opponents, we show that a variant of our optimistic MLE algorithm is capable of achieving sublinear regret when being compared against the optimal maximin policies.