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Under quite general conditions critical phenomena can be described with high order linked cluster expansions. The coefficients of the series admit a graphical expansion that is generated with the aid of computers. Our generalization of…

We consider the analysis of sets of categorical sequences consisting of piecewise homogeneous Markov segments. The sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each…

For sequential data, a change point is a moment of abrupt regime switch in data streams. Such changes appear in different scenarios, including simpler data from sensors and more challenging video surveillance data. We need to detect…

Many real-world time series, such as in health, have changepoints where the system's structure or parameters change. Since changepoints can indicate critical events such as onset of illness, it is highly important to detect them. However,…

Accelerating scientific discovery requires the identification of which experiments would yield the best outcomes before committing resources to costly physical validation. While existing benchmarks evaluate LLMs on scientific knowledge and…

Current frontier large-language models rely on reasoning to achieve state-of-the-art performance. Many existing interpretability are limited in this area, as standard methods have been designed to study single forward passes of a model…

Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested…

In this thesis, we explore the intersection of two fundamental subfields of quantum information theory: quantum coherence and contextuality. Despite their apparent differences, both areas address key issues relevant to the foundations and…

The objective of the change-point detection is to discover the abrupt property changes lying behind the time-series data. In this paper, we firstly summarize the definition and in-depth implication of the changepoint detection. The next…

Drug discovery is a complex process that involves sequentially screening and examining a vast array of molecules to identify those with the target properties. This process, also referred to as sequential experimentation, faces challenges…

The detection of anomalies in time series data is a critical task with many monitoring applications. Existing systems often fail to encompass an end-to-end detection process, to facilitate comparative analysis of various anomaly detection…

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…

We handle divergent {\epsilon} expansions in different universality classes derived from modified Landau-Wilson Hamiltonian. Landau-Wilson Hamiltonian can cater for describing critical phenomena on a wide range of physical systems which…

Attention matrices are fundamental to transformer research, supporting a broad range of applications including interpretability, visualization, manipulation, and distillation. Yet, most existing analyses focus on individual attention heads…

Causal inference is essential for data-driven decision making across domains such as business engagement, medical treatment and policy making. However, research on causal discovery has evolved separately from inference methods, preventing…

In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general…

Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…

Causality is vital for understanding true cause-and-effect relationships between variables within predictive models, rather than relying on mere correlations, making it highly relevant in the field of Explainable AI. In an automated…

Significance testing based on p-values has been implicated in the reproducibility crisis in scientific research, with one of the proposals being to eliminate them in favor of Bayesian analyses. Defenders of the p-values have countered that…

While instance-level explanation of GNN is a well-studied problem with plenty of approaches being developed, providing a global explanation for the behaviour of a GNN is much less explored, despite its potential in interpretability and…