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Matrix-product states (MPS) have proven to be a versatile ansatz for modeling quantum many-body physics. For many applications, and particularly in one-dimension, they capture relevant quantum correlations in many-body wavefunctions while…

A software library for constructing and learning probabilistic models is presented. The library offers a set of building blocks from which a large variety of static and dynamic models can be built. These include hierarchical models for…

Modern cryptographic methods for implementing privacy-preserving LLMs such as \gls{HE} require the LLMs to have a polynomial form. Forming such a representation is challenging because transformers include non-polynomial components, such as…

In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…

Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…

Long-term time series forecasting (LTSF) offers broad utility in practical settings like energy consumption and weather prediction. Accurately predicting long-term changes, however, is demanding due to the intricate temporal patterns and…

Ensemble learning has proven effective in boosting predictive performance, but traditional methods such as bagging, boosting, and dynamic ensemble selection (DES) suffer from high computational cost and limited adaptability to heterogeneous…

Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for…

In this paper, we propose a robust data-driven process model whose hyperparameters are robustly estimated using the Schweppe-type generalized maximum likelihood estimator. The proposed model is trained on recorded time-series data of…

Recently, a novel method based on coding partitions [1]-[4] has been used to derive power series expansions to previously intractable problems. In this method the coefficients at $k$ are determined by summing the contributions made by each…

When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…

Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied within machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for…

We discuss a new approach to realization of the well-known Weierstrass's programme on efficient continuation of an analytic element corresponding to a~multivalued analytic function with finite number of branch points. Our approach is based…

Amid mounting concern about the reliability and credibility of machine learning research, we present a principled framework for making robust and generalizable claims: the multiverse analysis. Our framework builds upon the multiverse…

Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6): 601-618, 2001) and Liu et al. (Circuits Syst. Signal Process. 30(3): 553-566, 2011), we investigate how to factorize a class of multivariate polynomial matrices. The…

Multi-agent reinforcement learning (MARL) methods struggle with the non-stationarity of multi-agent systems and fail to adaptively learn online when tested with novel agents. Here, we leverage large language models (LLMs) to create an…

Statistical power is a measure of the replicability of a categorical hypothesis test. Formally, it is the probability of detecting an effect, if there is a true effect present in the population. Hence, optimizing statistical power as a…

In production recommender systems, feature preprocessing must be faithfully replicated across training and inference environments. This often requires duplicating logic between offline and online environments, increasing engineering effort…

Multivariate Analysis is an increasingly common tool in experimental high energy physics; however, many of the common approaches were borrowed from other fields. We clarify what the goal of a multivariate algorithm should be for the search…

Reinforcement Learning (RL) is increasingly adopted to train agents that can deal with complex sequential tasks, such as driving an autonomous vehicle or controlling a humanoid robot. Correspondingly, novel approaches are needed to ensure…