Related papers: Optimal Discriminant Functions Based On Sampled Di…
Given samples from an unknown distribution $p$, is it possible to distinguish whether $p$ belongs to some class of distributions $\mathcal{C}$ versus $p$ being far from every distribution in $\mathcal{C}$? This fundamental question has…
A central topic in functional data analysis is how to design an optimaldecision rule, based on training samples, to classify a data function. We exploit the optimal classification problem when data functions are Gaussian processes. Sharp…
Distribution testing deals with what information can be deduced about an unknown distribution over $\{1,\ldots,n\}$, where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In…
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
Optimising discrete data for a desired characteristic using gradient-based methods involves projecting the data into a continuous latent space and carrying out optimisation in this space. Carrying out global optimisation is difficult as…
Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an…
Bias evaluation is fundamental to trustworthy AI, both in terms of checking data quality and in terms of checking the outputs of AI systems. In testing data quality, for example, one may study the distance of a given dataset, viewed as a…
This article investigates the probabilistic relationship between quantum classification of Boolean functions and their Hamming distance. By integrating concepts from quantum computing, information theory, and combinatorics, we explore how…
Machine learning techniques can reveal hidden structure in large data amounts and can potentially extent or even replace analytical scientific methods. In nanophotonics, modes can increase the light yield from emitters located inside the…
In this work we develop and implement a novel Bayesian method for computing the DOS of a system. This method is based on the use of a test function with adjustable parameters and we use Bayes theorem to find the best parameters given a…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
We address the problem of finding optimal strategies for computing Boolean symmetric functions. We consider a collocated network, where each node's transmissions can be heard by every other node. Each node has a Boolean measurement and we…
This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…
A novel approach is suggested for improving the accuracy of fault detection in distribution networks. This technique combines adaptive probability learning and waveform decomposition to optimize the similarity of features. Its objective is…
We address binary classification using neural ordinary differential equations from the perspective of simultaneous control of $N$ data points. We consider a single-neuron architecture with parameters fixed as piecewise constant functions of…
We study robust testing and estimation of discrete distributions in the strong contamination model. We consider both the "centralized setting" and the "distributed setting with information constraints" including communication and local…
We consider the problem of distributed estimation under the Bayesian criterion and explore the design of optimal quantizers in such a system. We show that, for a conditionally unbiased and efficient estimator at the fusion center and when…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
Object detection involves two sub-tasks, i.e. localizing objects in an image and classifying them into various categories. For existing CNN-based detectors, we notice the widespread divergence between localization and classification, which…
We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…