Extreme-mass-ratio inspiral (EMRI) signals pose significant challenges in gravitational wave (GW) astronomy owing to their low-frequency nature and highly complex waveforms, which occupy a high-dimensional parameter space with numerous variables. Given their extended inspiral timescales and low signal-to-noise ratios, EMRI signals warrant prolonged observation periods. Parameter estimation becomes particularly challenging due to non-local parameter degeneracies, arising from multiple local maxima, as well as flat regions and ridges inherent in the likelihood function. These factors lead to exceptionally high time complexity for parameter analysis while employing traditional matched filtering and random sampling methods. To address these challenges, the present study applies machine learning to Bayesian posterior estimation of EMRI signals, leveraging the recently developed flow matching technique based on ODE neural networks. Our approach demonstrates computational efficiency several orders of magnitude faster than the traditional Markov Chain Monte Carlo (MCMC) methods, while preserving the unbiasedness of parameter estimation. We show that machine learning technology has the potential to efficiently handle the vast parameter space, involving up to seventeen parameters, associated with EMRI signals. Furthermore, to our knowledge, this is the first instance of applying machine learning, specifically the Continuous Normalizing Flows (CNFs), to EMRI signal analysis. Our findings highlight the promising potential of machine learning in EMRI waveform analysis, offering new perspectives for the advancement of space-based GW detection and GW astronomy.

Regression is a fundamental prediction task common in data-centric engineering applications that involves learning mappings between continuous variables. In many engineering applications (e.g.\ structural health monitoring), feature-label pairs used to learn such mappings are of limited availability which hinders the effectiveness of traditional supervised machine learning approaches. The current paper proposes a methodology for overcoming the issue of data scarcity by combining active learning with hierarchical Bayesian modelling. Active learning is an approach for preferentially acquiring feature-label pairs in a resource-efficient manner. In particular, the current work adopts a risk-informed approach that leverages contextual information associated with regression-based engineering decision-making tasks (e.g.\ inspection and maintenance). Hierarchical Bayesian modelling allow multiple related regression tasks to be learned over a population, capturing local and global effects. The information sharing facilitated by this modelling approach means that information acquired for one engineering system can improve predictive performance across the population. The proposed methodology is demonstrated using an experimental case study. Specifically, multiple regressions are performed over a population of machining tools, where the quantity of interest is the surface roughness of the workpieces. An inspection and maintenance decision process is defined using these regression tasks which is in turn used to construct the active-learning algorithm. The novel methodology proposed is benchmarked against an uninformed approach to label acquisition and independent modelling of the regression tasks. It is shown that the proposed approach has superior performance in terms of expected cost -- maintaining predictive performance while reducing the number of inspections required.

This paper presents a game theoretic formulation of a graph traversal problem, with applications to robots moving through hazardous environments in the presence of an adversary, as in military and security applications. The blue team of robots moves in an environment modeled by a time-varying graph, attempting to reach some goal with minimum cost, while the red team controls how the graph changes to maximize the cost. The problem is formulated as a stochastic game, so that Nash equilibrium strategies can be computed numerically. Bounds are provided for the game value, with a guarantee that it solves the original problem. Numerical simulations demonstrate the results and the effectiveness of this method, particularly showing the benefit of mixing actions for both players, as well as beneficial coordinated behavior, where blue robots split up and/or synchronize to traverse risky edges.

To make sense of massive data, we often first fit simplified models and then interpret the parameters; for example, we cluster the text embeddings and then interpret the mean parameters of each cluster. However, these parameters are often highdimensional and hard to interpret. To make model parameters directly interpretable, we introduce a family of statistical models--including clustering, time series, and classification models--parameterized by natural language predicates. For example, a cluster of text about COVID could be parameterized by the predicate "discusses COVID". To learn these statistical models effectively, we develop a model-agnostic algorithm that optimizes continuous relaxations of predicate parameters with gradient descent and discretizes them by prompting language models (LMs). Finally, we apply our framework to a wide range of problems: taxonomizing user chat dialogues, characterizing how they evolve across time, finding categories where one language model is better than the other, clustering math problems based on subareas, and explaining visual features in memorable images. Our framework is highly versatile, applicable to both textual and visual domains, can be easily steered to focus on specific properties (e.g.

We address the problem of learning the topology of directed acyclic graphs (DAGs) from nodal observations, which adhere to a linear structural equation model. Recent advances framed the combinatorial DAG structure learning task as a continuous optimization problem, yet existing methods must contend with the complexities of non-convex optimization. To overcome this limitation, we assume that the latent DAG contains only non-negative edge weights. Leveraging this additional structure, we argue that cycles can be effectively characterized (and prevented) using a convex acyclicity function based on the log-determinant of the adjacency matrix. This convexity allows us to relax the task of learning the non-negative weighted DAG as an abstract convex optimization problem. We propose a DAG recovery algorithm based on the method of multipliers, that is guaranteed to return a global minimizer. Furthermore, we prove that in the infinite sample size regime, the convexity of our approach ensures the recovery of the true DAG structure. We empirically validate the performance of our algorithm in several reproducible synthetic-data test cases, showing that it outperforms state-of-the-art alternatives.

We present a lightweight approach to sequence classification using Ensemble Methods for Hidden Markov Models (HMMs). HMMs offer significant advantages in scenarios with imbalanced or smaller datasets due to their simplicity, interpretability, and efficiency. These models are particularly effective in domains such as finance and biology, where traditional methods struggle with high feature dimensionality and varied sequence lengths. Our ensemble-based scoring method enables the comparison of sequences of any length and improves performance on imbalanced datasets. This study focuses on the binary classification problem, particularly in scenarios with data imbalance, where the negative class is the majority (e.g., normal data) and the positive class is the minority (e.g., anomalous data), often with extreme distribution skews. We propose a novel training approach for HMM Ensembles that generalizes to multi-class problems and supports classification and anomaly detection. Our method fits class-specific groups of diverse models using random data subsets, and compares likelihoods across classes to produce composite scores, achieving high average precisions and AUCs. In addition, we compare our approach with neural network-based methods such as Convolutional Neural Networks (CNNs) and Long Short-Term Memory networks (LSTMs), highlighting the efficiency and robustness of HMMs in data-scarce environments. Motivated by real-world use cases, our method demonstrates robust performance across various benchmarks, offering a flexible framework for diverse applications.

Value at Risk (VaR) and stress testing are two of the most widely used approaches in portfolio risk management to estimate potential market value losses under adverse market moves. VaR quantifies potential loss in value over a specified horizon (such as one day or ten days) at a desired confidence level (such as 95'th percentile). In scenario design and stress testing, the goal is to construct extreme market scenarios such as those involving severe recession or a specific event of concern (such as a rapid increase in rates or a geopolitical event), and quantify potential impact of such scenarios on the portfolio. The goal of this paper is to propose an approach for incorporating prevailing market conditions in stress scenario design and estimation of VaR so that they provide more accurate and realistic insights about portfolio risk over the near term. The proposed approach is based on historical data where historical observations of market changes are given more weight if a certain period in history is "more similar" to the prevailing market conditions. Clusters of market conditions are identified using a Machine Learning approach called Variational Inference (VI) where for each cluster future changes in portfolio value are similar. VI based algorithm uses optimization techniques to obtain analytical approximations of the posterior probability density of cluster assignments (market regimes) and probabilities of different outcomes for changes in portfolio value. Covid related volatile period around the year 2020 is used to illustrate the performance of the proposed approach and in particular show how VaR and stress scenarios adapt quickly to changing market conditions. Another advantage of the proposed approach is that classification of market conditions into clusters can provide useful insights about portfolio performance under different market conditions.

Inverse Constrained Reinforcement Learning (ICRL) is the task of inferring the implicit constraints followed by expert agents from their demonstration data. As an emerging research topic, ICRL has received considerable attention in recent years. This article presents a categorical survey of the latest advances in ICRL. It serves as a comprehensive reference for machine learning researchers and practitioners, as well as starters seeking to comprehend the definitions, advancements, and important challenges in ICRL. We begin by formally defining the problem and outlining the algorithmic framework that facilitates constraint inference across various scenarios. These include deterministic or stochastic environments, environments with limited demonstrations, and multiple agents. For each context, we illustrate the critical challenges and introduce a series of fundamental methods to tackle these issues. This survey encompasses discrete, virtual, and realistic environments for evaluating ICRL agents. We also delve into the most pertinent applications of ICRL, such as autonomous driving, robot control, and sports analytics. To stimulate continuing research, we conclude the survey with a discussion of key unresolved questions in ICRL that can effectively foster a bridge between theoretical understanding and practical industrial applications.

Merging datasets across institutions is a lengthy and costly procedure, especially when it involves private information. Data hosts may therefore want to prospectively gauge which datasets are most beneficial to merge with, without revealing sensitive information. For causal estimation this is particularly challenging as the value of a merge will depend not only on the reduction in epistemic uncertainty but also the improvement in overlap. To address this challenge, we introduce the first cryptographically secure information-theoretic approach for quantifying the value of a merge in the context of heterogeneous treatment effect estimation. We do this by evaluating the Expected Information Gain (EIG) and utilising multi-party computation to ensure it can be securely computed without revealing any raw data. As we demonstrate, this can be used with differential privacy (DP) to ensure privacy requirements whilst preserving more accurate computation than naive DP alone. To the best of our knowledge, this work presents the first privacy-preserving method for dataset acquisition tailored to causal estimation. We demonstrate the effectiveness and reliability of our method on a range of simulated and realistic benchmarks. The code is available anonymously.

In feed-forward neural networks, dataset-free weight-initialization method such as LeCun, Xavier (or Glorot), and He initializations have been developed. These methods randomly determine the initial values of weight parameters based on specific distributions (e.g., Gaussian or uniform distributions) without using training datasets. To the best of the authors' knowledge, such a dataset-free weight-initialization method is yet to be developed for restricted Boltzmann machines (RBMs), which are probabilistic neural networks consisting of two layers, In this study, we derive a dataset-free weight-initialization method for Bernoulli--Bernoulli RBMs based on a statistical mechanical analysis. In the proposed weight-initialization method, the weight parameters are drawn from a Gaussian distribution with zero mean. The standard deviation of the Gaussian distribution is optimized based on our hypothesis which is that a standard deviation providing a larger layer correlation (LC) between the two layers improves the learning efficiency. The expression of the LC is derived based on a statistical mechanical analysis. The optimal value of the standard deviation corresponds to the maximum point of the LC. The proposed weight-initialization method is identical to Xavier initialization in a specific case (i.e., in the case the sizes of the two layers are the same, the random variables of the layers are $\{-1,1\}$-binary, and all bias parameters are zero).