Related papers: Differentiability and overlap concentration in opt…
Consider a two-class classification problem where the number of features is much larger than the sample size. The features are masked by Gaussian noise with mean zero and covariance matrix $\Sigma$, where the precision matrix…
Optimization constrained by high-fidelity computational models has potential for transformative impact. However, such optimization is frequently unattainable in practice due to the complexity and computational intensity of the model. An…
Bayesian optimal sensor placement, in its full generality, seeks to maximize the mutual information between uncertain model parameters and the predicted data to be collected from the sensors for the purpose of performing Bayesian inference.…
The focusing operation inherent to the linear discrete inverse problem is formalised. The development is given in the context of sound-field reproduction where the source strengths are the inverse solution needed to recreate a prescribed…
In this paper we construct optimal designs for frequentist model averaging estimation. We derive the asymptotic distribution of the model averaging estimate with fixed weights in the case where the competing models are non-nested and none…
Sensor calibration is an indispensable task in any networked cyberphysical system. In this paper, we consider a sensor network plagued with offset errors, measuring a rank-1 signal subspace, where each sensor collects measurements under a…
A simple strategy for improving LLM accuracy, especially in math and reasoning problems, is to sample multiple responses and submit the answer most consistently reached. In this paper we leverage Bayesian prior information to save on…
Determining the best model or models for a particular data set, a process known as Bayesian model comparison, is a critical part of probabilistic inference. Typically, this process assumes a fixed model-space (that is, a fixed set of…
The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…
We prove anti-concentration bounds for the inner product of two independent random vectors, and use these bounds to prove lower bounds in communication complexity. We show that if $A,B$ are subsets of the cube $\{\pm 1\}^n$ with $|A| \cdot…
The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular…
We study a class of binary detection problems involving a single fusion center and a large or countably infinite number of sensors. Each sensor acts under a decentralized information structure, accessing only a local noisy observation…
We give new characterizations of the sample complexity of answering linear queries (statistical queries) in the local and central models of differential privacy: *In the non-interactive local model, we give the first approximate…
Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of…
This work explores multi-modal inference in a high-dimensional simplified model, analytically quantifying the performance gain of multi-modal inference over that of analyzing modalities in isolation. We present the Bayes-optimal performance…
To optimize efficiently over discrete data and with only few available target observations is a challenge in Bayesian optimization. We propose a continuous relaxation of the objective function and show that inference and optimization can be…
We consider rank-one symmetric tensor estimation when the tensor is corrupted by Gaussian noise and the spike forming the tensor is a structured signal coming from a generalized linear model. The latter is a mathematically tractable model…
Model fitting is possibly the most extended problem in science. Classical approaches include the use of least-squares fitting procedures and maximum likelihood methods to estimate the value of the parameters in the model. However, in recent…
Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…
The lossless data compression algorithm based on Bayesian Attention Networks is derived from first principles. Bayesian Attention Networks are defined by introducing an attention factor per a training sample loss as a function of two sample…