Related papers: Projection Pursuit through $\Phi$-Divergence Minim…
We introduce the first differentiable approximation of range-partition entropy, a complexity measure from computational geometry that directly bounds algorithmic runtime. Unlike architectural modifications, our method is a complementary…
This paper proposes a probabilistic approach for the detection and the tracking of particles in fluorescent time-lapse imaging. In the presence of a very noised and poor-quality data, particles and trajectories can be characterized by an a…
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…
This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one…
We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor…
This paper proposes a clustering and merging approach for the Poisson multi-Bernoulli mixture (PMBM) filter to lower its computational complexity and make it suitable for multiple target tracking with a high number of targets. We define a…
Although there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated…
In multi-target tracking, a data association hypothesis assigns measurements to tracks, and the hypothesis likelihood (of the joint target-measurement associations) is used to compare among all hypotheses for truncation under a finite…
Two goodness-of-fit tests for copulas are being investigated. The first one deals with the case of elliptical copulas and the second one deals with independent copulas. These tests result from the expansion of the projection pursuit…
The project of physics discovery is often equivalent to finding the most concise description of a physical system. The description with optimum predictive capability for a dataset generated by a physical system is one that minimizes both…
We consider an extension of $\epsilon$-entropy to a KL-divergence based complexity measure for randomized density estimation methods. Based on this extension, we develop a general information-theoretical inequality that measures the…
We analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We consider the standard forward uncertainty quantification problem where an assumed probability density on…
Given a probability measure with density, Fermat distances and density-driven metrics are conformal transformations of the Euclidean metric that shrink distances in high density areas and enlarge distances in low density areas. Although…
Reducing hidden bias in the data and ensuring fairness in algorithmic data analysis has recently received significant attention. We complement several recent papers in this line of research by introducing a general method to reduce bias in…
Density power divergence (DPD) is designed to robustly estimate the underlying distribution of observations, in the presence of outliers. However, DPD involves an integral of the power of the parametric density models to be estimated; the…
Interactive visualization of embedding projections is a useful technique for understanding data and evaluating machine learning models. Labeling data within these visualizations is critical for interpretation, as labels provide an overview…
Calibration methods have been widely studied in survey sampling over the last decades. Viewing calibration as an inverse problem, we extend the calibration technique by using a maximum entropy method. Finding the optimal weights is achieved…
In this paper, we introduce a geometric framework to analyze memorization in diffusion models through the sharpness of the log probability density. We mathematically justify a previously proposed score-difference-based memorization metric…
In the past decade, matrix factorization has been extensively researched and has become one of the most popular techniques for personalized recommendations. Nevertheless, the dot product adopted in matrix factorization based recommender…