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Interpretability is a pressing issue for machine learning. Common approaches to interpretable machine learning constrain interactions between features of the input, rendering the effects of those features on a model's output comprehensible…
Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…
We consider minimax-optimal designs for the prediction of individual parameters in random coefficient regression models. We focus on the minimax-criterion, which minimizes the "worst case" for the basic criterion with respect to the…
The principle of Maximal Coding Rate Reduction (MCR$^2$) has recently been proposed as a training objective for learning discriminative low-dimensional structures intrinsic to high-dimensional data to allow for more robust training than…
We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…
We introduce a method to determine if a certain capability helps to achieve an accurate model of given data. We view labels as being generated from the inputs by a program composed of subroutines with different capabilities, and we posit…
In this paper we present a simple partitioning based technique to refine the statistical analysis of classification algorithms. The core of our idea is to divide the input space into two parts such that the first part contains a suitable…
A fundamental problem associated with the task of network reconstruction from dynamical or behavioral data consists in determining the most appropriate model complexity in a manner that prevents overfitting, and produces an inferred network…
The framework of Partial Information Decomposition (PID) unveils complex nonlinear interactions in network systems by dissecting the mutual information (MI) between a target variable and several source variables. While PID measures have…
Algorithms for machine learning-guided design, or design algorithms, use machine learning-based predictions to propose novel objects with desired property values. Given a new design task -- for example, to design novel proteins with high…
We present the theory of linear rank-metric codes from the point of view of their fundamental parameters. These are: the minimum rank distance, the rank distribution, the maximum rank, the covering radius, and the field size. The focus of…
The International Classification of Diseases (ICD) is an authoritative medical classification system of different diseases and conditions for clinical and management purposes. ICD indexing assigns a subset of ICD codes to a medical record.…
The continually increasing number of complex datasets each year necessitates ever improving machine learning methods for robust and accurate categorization of these data. This paper introduces Random Multimodel Deep Learning (RMDL): a new…
Information criteria such as Akaike's (AIC) and Bayes' (BIC) are widely used for model selection in physics and beyond, quantifying the tradeoff between model complexity and goodness-of-fit to enforce parsimony. However, their derivation…
Attribution methods provide insights into the decision-making of machine learning models like artificial neural networks. For a given input sample, they assign a relevance score to each individual input variable, such as the pixels of an…
The Akaike information criterion (AIC) is commonly used to select a logistic regression model for optimal prediction of a binary response by a specified family of models. It however lacks a convincing method of prescribing a proper family…
Large Language Models (LLMs) are a powerful tool for statistical text analysis, with derived sequences of next-token probability distributions offering a wealth of information. Extracting this signal typically relies on metrics such as…
Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association…
Robust model-fitting to spectroscopic transitions is a requirement across many fields of science. The corrected Akaike and Bayesian information criteria (AICc and BIC) are most frequently used to select the optimal number of fitting…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…