This paper analyzes multi-step TD-learning algorithms within the `deadly triad' scenario, characterized by linear function approximation, off-policy learning, and bootstrapping. In particular, we prove that n-step TD-learning algorithms converge to a solution as the sampling horizon n increases sufficiently. The paper is divided into two parts. In the first part, we comprehensively examine the fundamental properties of their model-based deterministic counterparts, including projected value iteration, gradient descent algorithms, and the control theoretic approach, which can be viewed as prototype deterministic algorithms whose analysis plays a pivotal role in understanding and developing their model-free reinforcement learning counterparts. In particular, we prove that these algorithms converge to meaningful solutions when n is sufficiently large. Based on these findings, two n-step TD-learning algorithms are proposed and analyzed, which can be seen as the model-free reinforcement learning counterparts of the gradient and control theoretic algorithms.

Bayesian optimal experimental design (OED) seeks experiments that maximize the expected information gain (EIG) in model parameters. Directly estimating the EIG using nested Monte Carlo is computationally expensive and requires an explicit likelihood. Variational OED (vOED), in contrast, estimates a lower bound of the EIG without likelihood evaluations by approximating the posterior distributions with variational forms, and then tightens the bound by optimizing its variational parameters. We introduce the use of normalizing flows (NFs) for representing variational distributions in vOED; we call this approach vOED-NFs. Specifically, we adopt NFs with a conditional invertible neural network architecture built from compositions of coupling layers, and enhanced with a summary network for data dimension reduction. We present Monte Carlo estimators to the lower bound along with gradient expressions to enable a gradient-based simultaneous optimization of the variational parameters and the design variables. The vOED-NFs algorithm is then validated in two benchmark problems, and demonstrated on a partial differential equation-governed application of cathodic electrophoretic deposition and an implicit likelihood case with stochastic modeling of aphid population. The findings suggest that a composition of 4--5 coupling layers is able to achieve lower EIG estimation bias, under a fixed budget of forward model runs, compared to previous approaches. The resulting NFs produce approximate posteriors that agree well with the true posteriors, able to capture non-Gaussian and multi-modal features effectively.

Characterization of joint probability distribution for large networks of random variables remains a challenging task in data science. Probabilistic graph approximation with simple topologies has practically been resorted to; typically the tree topology makes joint probability computation much simpler and can be effective for statistical inference on insufficient data. However, to characterize network components where multiple variables cooperate closely to influence others, model topologies beyond a tree are needed, which unfortunately are infeasible to acquire. In particular, our previous work has related optimal approximation of Markov networks of tree-width k >=2 closely to the graph-theoretic problem of finding maximum spanning k-tree (MSkT), which is a provably intractable task. This paper investigates optimal approximation of Markov networks with k-tree topology that retains some designated underlying subgraph. Such a subgraph may encode certain background information that arises in scientific applications, for example, about a known significant pathway in gene networks or the indispensable backbone connectivity in the residue interaction graphs for a biomolecule 3D structure. In particular, it is proved that the \beta-retaining MSkT problem, for a number of classes \beta of graphs, admit O(n^{k+1})-time algorithms for every fixed k>= 1. These \beta-retaining MSkT algorithms offer efficient solutions for approximation of Markov networks with k-tree topology in the situation where certain persistent information needs to be retained.

Missing data poses a significant challenge in data science, affecting decision-making processes and outcomes. Understanding what missing data is, how it occurs, and why it is crucial to handle it appropriately is paramount when working with real-world data, especially in tabular data, one of the most commonly used data types in the real world. Three missing mechanisms are defined in the literature: Missing Completely At Random (MCAR), Missing At Random (MAR), and Missing Not At Random (MNAR), each presenting unique challenges in imputation. Most existing work are focused on MCAR that is relatively easy to handle. The special missing mechanisms of MNAR and MAR are less explored and understood. This article reviews existing literature on handling missing values. It compares and contrasts existing methods in terms of their ability to handle different missing mechanisms and data types. It identifies research gap in the existing literature and lays out potential directions for future research in the field. The information in this review will help data analysts and researchers to adopt and promote good practices for handling missing data in real-world problems.

The domain of online learning has experienced multifaceted expansion owing to its prevalence in real-life applications. Nonetheless, this progression operates under the assumption that the input feature space of the streaming data remains constant. In this survey paper, we address the topic of online learning in the context of haphazard inputs, explicitly foregoing such an assumption. We discuss, classify, evaluate, and compare the methodologies that are adept at modeling haphazard inputs, additionally providing the corresponding code implementations and their carbon footprint. Moreover, we classify the datasets related to the field of haphazard inputs and introduce evaluation metrics specifically designed for datasets exhibiting imbalance. The code of each methodology can be found at https://github.com/Rohit102497/HaphazardInputsReview

The discovery of causal relationships from observational data is very challenging. Many recent approaches rely on complexity or uncertainty concepts to impose constraints on probability distributions, aiming to identify specific classes of directed acyclic graph (DAG) models. In this paper, we introduce a novel identifiability criterion for DAGs that places constraints on the conditional variances of additive noise models. We demonstrate that this criterion extends and generalizes existing identifiability criteria in the literature that employ (conditional) variances as measures of uncertainty in (conditional) distributions. For linear Structural Equation Models, we present a new algorithm that leverages the concept of weak majorization applied to the diagonal elements of the Cholesky factor of the covariance matrix to learn a topological ordering of variables. Through extensive simulations and the analysis of bank connectivity data, we provide evidence of the effectiveness of our approach in successfully recovering DAGs. The code for reproducing the results in this paper is available in Supplementary Materials.

Breast cancer has rapidly increased in prevalence in recent years, making it one of the leading causes of mortality worldwide. Among all cancers, it is by far the most common. Diagnosing this illness manually requires significant time and expertise. Since detecting breast cancer is a time-consuming process, preventing its further spread can be aided by creating machine-based forecasts. Machine learning and Explainable AI are crucial in classification as they not only provide accurate predictions but also offer insights into how the model arrives at its decisions, aiding in the understanding and trustworthiness of the classification results. In this study, we evaluate and compare the classification accuracy, precision, recall, and F-1 scores of five different machine learning methods using a primary dataset (500 patients from Dhaka Medical College Hospital). Five different supervised machine learning techniques, including decision tree, random forest, logistic regression, naive bayes, and XGBoost, have been used to achieve optimal results on our dataset. Additionally, this study applied SHAP analysis to the XGBoost model to interpret the model's predictions and understand the impact of each feature on the model's output. We compared the accuracy with which several algorithms classified the data, as well as contrasted with other literature in this field. After final evaluation, this study found that XGBoost achieved the best model accuracy, which is 97%.

This paper presents different neural network-based classifier algorithms for diagnosing and classifying Anemia. The study compares these classifiers with established models such as Feed Forward Neural Network (FFNN), Elman network, and Non-linear Auto-Regressive Exogenous model (NARX). Experimental evaluations were conducted using data from clinical laboratory test results for 230 patients. The proposed neural network features nine inputs (age, gender, RBC, HGB, HCT, MCV, MCH, MCHC, WBCs) and one output. The simulation outcomes for diverse patients demonstrate that the suggested artificial neural network rapidly and accurately detects the presence of the disease. Consequently, the network could be seamlessly integrated into clinical laboratories for automatic generation of Anemia patients' reports Additionally, the suggested method is affordable and can be deployed on hardware at low costs.

Despite tremendous advancements in large language models (LLMs) over recent years, a notably urgent challenge for their practical deployment is the phenomenon of hallucination, where the model fabricates facts and produces non-factual statements. In response, we propose PoLLMgraph, a Polygraph for LLMs, as an effective model-based white-box detection and forecasting approach. PoLLMgraph distinctly differs from the large body of existing research that concentrates on addressing such challenges through black-box evaluations. In particular, we demonstrate that hallucination can be effectively detected by analyzing the LLM's internal state transition dynamics during generation via tractable probabilistic models. Experimental results on various open-source LLMs confirm the efficacy of PoLLMgraph, outperforming state-of-the-art methods by a considerable margin, evidenced by over 20% improvement in AUC-ROC on common benchmarking datasets like TruthfulQA. Our work paves a new way for model-based white-box analysis of LLMs, motivating the research community to further explore, understand, and refine the intricate dynamics of LLM behaviors.

The remarkable generalization performance of overparameterized models has challenged the conventional wisdom of statistical learning theory. While recent theoretical studies have shed light on this behavior in linear models or nonlinear classifiers, a comprehensive understanding of overparameterization in nonlinear regression models remains lacking. This paper explores the predictive properties of overparameterized nonlinear regression within the Bayesian framework, extending the methodology of adaptive prior based on the intrinsic spectral structure of the data. We establish posterior contraction for single-neuron models with Lipschitz continuous activation functions and for generalized linear models, demonstrating that our approach achieves consistent predictions in the overparameterized regime. Moreover, our Bayesian framework allows for uncertainty estimation of the predictions. The proposed method is validated through numerical simulations and a real data application, showcasing its ability to achieve accurate predictions and reliable uncertainty estimates. Our work advances the theoretical understanding of the blessing of overparameterization and offers a principled Bayesian approach for prediction in large nonlinear models.