In recent years, machine learning has witnessed extensive adoption across various sectors, yet its application in medical image-based disease detection and diagnosis remains challenging due to distribution shifts in real-world data. In practical settings, deployed models encounter samples that differ significantly from the training dataset, especially in the health domain, leading to potential performance issues. This limitation hinders the expressiveness and reliability of deep learning models in health applications. Thus, it becomes crucial to identify methods capable of producing reliable uncertainty estimation in the context of distribution shifts in the health sector. In this paper, we explore the feasibility of using cutting-edge Bayesian and non-Bayesian methods to detect distributionally shifted samples, aiming to achieve reliable and trustworthy diagnostic predictions in segmentation task. Specifically, we compare three distinct uncertainty estimation methods, each designed to capture either unimodal or multimodal aspects in the posterior distribution. Our findings demonstrate that methods capable of addressing multimodal characteristics in the posterior distribution, offer more dependable uncertainty estimates. This research contributes to enhancing the utility of deep learning in healthcare, making diagnostic predictions more robust and trustworthy.

Denoising Diffusion Probabilistic Models (DDPMs) [Ho et al., 2020] are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis, weather forecasting, and neural surrogates of partial differential equations. Despite their ubiquity it is hard to find an introduction to DDPMs which is simple, comprehensive, clean and clear. The compact explanations necessary in research papers are not able to elucidate all of the different design steps taken to formulate the DDPM and the rationale of the steps that are presented is often omitted to save space. Moreover, the expositions are typically presented from the variational lower bound perspective which is unnecessary and arguably harmful as it obfuscates why the method is working and suggests generalisations that do not perform well in practice. On the other hand, perspectives that take the continuous time-limit are beautiful and general, but they have a high barrier-to-entry as they require background knowledge of stochastic differential equations and probability flow. In this note, we distill down the formulation of the DDPM into six simple steps each of which comes with a clear rationale. We assume that the reader is familiar with fundamental topics in machine learning including basic probabilistic modelling, Gaussian distributions, maximum likelihood estimation, and deep learning.

Geosteering, a key component of drilling operations, traditionally involves manual interpretation of various data sources such as well-log data. This introduces subjective biases and inconsistent procedures. Academic attempts to solve geosteering decision optimization with greedy optimization and Approximate Dynamic Programming (ADP) showed promise but lacked adaptivity to realistic diverse scenarios. Reinforcement learning (RL) offers a solution to these challenges, facilitating optimal decision-making through reward-based iterative learning. State estimation methods, e.g., particle filter (PF), provide a complementary strategy for geosteering decision-making based on online information. We integrate an RL-based geosteering with PF to address realistic geosteering scenarios. Our framework deploys PF to process real-time well-log data to estimate the location of the well relative to the stratigraphic layers, which then informs the RL-based decision-making process. We compare our method's performance with that of using solely either RL or PF. Our findings indicate a synergy between RL and PF in yielding optimized geosteering decisions.

Adaptive behavior often requires predicting future events. The theory of reinforcement learning prescribes what kinds of predictive representations are useful and how to compute them. This paper integrates these theoretical ideas with work on cognition and neuroscience. We pay special attention to the successor representation (SR) and its generalizations, which have been widely applied both as engineering tools and models of brain function. This convergence suggests that particular kinds of predictive representations may function as versatile building blocks of intelligence.

This paper introduces the Quantified Boolean Bayesian Network (QBBN), which provides a unified view of logical and probabilistic reasoning. The QBBN is meant to address a central problem with the Large Language Model (LLM), which has become extremely popular in Information Retrieval, which is that the LLM hallucinates. A Bayesian Network, by construction, cannot hallucinate, because it can only return answers that it can explain. We show how a Bayesian Network over an unbounded number of boolean variables can be configured to represent the logical reasoning underlying human language. We do this by creating a key-value version of the First-Order Calculus, for which we can prove consistency and completeness. We show that the model is trivially trained over fully observed data, but that inference is non-trivial. Exact inference in a Bayesian Network is intractable (i.e. $\Omega(2^N)$ for $N$ variables). For inference, we investigate the use of Loopy Belief Propagation (LBP), which is not guaranteed to converge, but which has been shown to often converge in practice. Our experiments show that LBP indeed does converge very reliably, and our analysis shows that a round of LBP takes time $O(N2^n)$, where $N$ bounds the number of variables considered, and $n$ bounds the number of incoming connections to any factor, and further improvements may be possible. Our network is specifically designed to alternate between AND and OR gates in a Boolean Algebra, which connects more closely to logical reasoning, allowing a completeness proof for an expanded version of our network, and also allows inference to follow specific but adequate pathways, that turn out to be fast.

A decision tree is one of the most popular approaches in machine learning fields. However, it suffers from the problem of overfitting caused by overly deepened trees. Then, a meta-tree is recently proposed. It solves the problem of overfitting caused by overly deepened trees. Moreover, the meta-tree guarantees statistical optimality based on Bayes decision theory. Therefore, the meta-tree is expected to perform better than the decision tree. In contrast to a single decision tree, it is known that ensembles of decision trees, which are typically constructed boosting algorithms, are more effective in improving predictive performance. Thus, it is expected that ensembles of meta-trees are more effective in improving predictive performance than a single meta-tree, and there are no previous studies that construct multiple meta-trees in boosting. Therefore, in this study, we propose a method to construct multiple meta-trees using a boosting approach. Through experiments with synthetic and benchmark datasets, we conduct a performance comparison between the proposed methods and the conventional methods using ensembles of decision trees. Furthermore, while ensembles of decision trees can cause overfitting as well as a single decision tree, experiments confirmed that ensembles of meta-trees can prevent overfitting due to the tree depth.

We develop optimal algorithms for learning undirected Gaussian trees and directed Gaussian polytrees from data. We consider both problems of distribution learning (i.e. in KL distance) and structure learning (i.e. exact recovery). The first approach is based on the Chow-Liu algorithm, and learns an optimal tree-structured distribution efficiently. The second approach is a modification of the PC algorithm for polytrees that uses partial correlation as a conditional independence tester for constraint-based structure learning. We derive explicit finite-sample guarantees for both approaches, and show that both approaches are optimal by deriving matching lower bounds. Additionally, we conduct numerical experiments to compare the performance of various algorithms, providing further insights and empirical evidence.

Time Series Supplier Allocation (TSSA) poses a complex NP-hard challenge, aimed at refining future order dispatching strategies to satisfy order demands with maximum supply efficiency fully. Traditionally derived from financial portfolio management, the Black-Litterman (BL) model offers a new perspective for the TSSA scenario by balancing expected returns against insufficient supply risks. However, its application within TSSA is constrained by the reliance on manually constructed perspective matrices and spatio-temporal market dynamics, coupled with the absence of supervisory signals and data unreliability inherent to supplier information. To solve these limitations, we introduce the pioneering Deep Black-Litterman Model (DBLM), which innovatively adapts the BL model from financial roots to supply chain context. Leveraging the Spatio-Temporal Graph Neural Networks (STGNNS), DBLM automatically generates future perspective matrices for TSSA, by integrating spatio-temporal dependency. Moreover, a novel Spearman rank correlation distinctively supervises our approach to address the lack of supervisory signals, specifically designed to navigate through the complexities of supplier risks and interactions. This is further enhanced by a masking mechanism aimed at counteracting the biases from unreliable data, thereby improving the model's precision and reliability. Extensive experimentation on two datasets unequivocally demonstrates DBLM's enhanced performance in TSSA, setting new standards for the field. Our findings and methodology are made available for community access and further development.

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant $n$-body particle systems. We show that the proposed approach achieves state-of-the-art performance on all metrics and trains $2-5\times$ faster, which allows it to be the first method to train using energy on the challenging $55$-particle Lennard-Jones system.

In this work, we propose to tackle the problem of domain generalization in the context of \textit{insufficient samples}. Instead of extracting latent feature embeddings based on deterministic models, we propose to learn a domain-invariant representation based on the probabilistic framework by mapping each data point into probabilistic embeddings. Specifically, we first extend empirical maximum mean discrepancy (MMD) to a novel probabilistic MMD that can measure the discrepancy between mixture distributions (i.e., source domains) consisting of a series of latent distributions rather than latent points. Moreover, instead of imposing the contrastive semantic alignment (CSA) loss based on pairs of latent points, a novel probabilistic CSA loss encourages positive probabilistic embedding pairs to be closer while pulling other negative ones apart. Benefiting from the learned representation captured by probabilistic models, our proposed method can marriage the measurement on the \textit{distribution over distributions} (i.e., the global perspective alignment) and the distribution-based contrastive semantic alignment (i.e., the local perspective alignment). Extensive experimental results on three challenging medical datasets show the effectiveness of our proposed method in the context of insufficient data compared with state-of-the-art methods.