Related papers: Sparse-limit approximation for t-statistics

Across the empirical sciences, few statistical procedures rival the popularity of the frequentist t-test. In contrast, the Bayesian versions of the t-test have languished in obscurity. In recent years, however, the theoretical and practical…

We establish exact asymptotic expressions for the normalized mutual information and minimum mean-square-error (MMSE) of sparse linear regression in the sub-linear sparsity regime. Our result is achieved by a generalization of the adaptive…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

We consider the prediction of weak effects in a multiple-output regression setup, when covariates are expected to explain a small amount, less than $\approx 1%$, of the variance of the target variables. To facilitate the prediction of the…

Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…

Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…

We consider the counting rate estimation of an unknown radioactive source, which emits photons at times modeled by an homogeneous Poisson process. A spectrometer converts the energy of incoming photons into electrical pulses, whose number…

Active learning enables efficient model training by leveraging interactions between machine learning agents and human annotators. We study and propose a novel framework that formulates batch active learning from the sparse approximation's…

In the sparse normal means model, convergence of the Bayesian posterior distribution associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…

We study the problem of sampling a random signal with sparse support in frequency domain. Shannon famously considered a scheme that instantaneously samples the signal at equispaced times. He proved that the signal can be reconstructed as…

In this work we show a Bayesian quantile regression method to response variables with mixed discrete-continuous distribution with a point mass at zero, where these observations are believed to be left censored or true zeros. We combine the…

A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity,…

We analyze the distribution of the signal to noise ratio (SNR) loss at the output of an adaptive filter which is trained with samples that do not share the same covariance matrix as the samples for which the filter is foreseen. Our…

Semi-supervised learning (SSL) uses unlabeled data for training and has been shown to greatly improve performance when compared to a supervised approach on the labeled data available. This claim depends both on the amount of labeled data…

Sharpe ratio is widely used in asset management to compare and benchmark funds and asset managers. It computes the ratio of the excess return over the strategy standard deviation. However, the elements to compute the Sharpe ratio, namely,…

Semi-supervised learning on real-world graphs is frequently challenged by heterophily, where the observed graph is unreliable or label-disassortative. Many existing graph neural networks either rely on a fixed adjacency structure or attempt…

Random Effects analysis has been introduced into fMRI research in order to generalize findings from the study group to the whole population. Generalizing findings is obviously harder than detecting activation in the study group since in…

Computing ratios of normalizing constants plays an important role in statistical modeling. Two important examples are hypothesis testing in latent variables models, and model comparison in Bayesian statistics. In both examples, the…

A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…

Let $(X,Y)\in\mathcal{X}\times \mathcal{Y}$ be a random couple with unknown distribution $P$. Let $\GG$ be a class of measurable functions and $\ell$ a loss function. The problem of statistical learning deals with the estimation of the…