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We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. We propose to jointly estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss…

Incorporating encoding-decoding nets with adversarial nets has been widely adopted in image generation tasks. We observe that the state-of-the-art achievements were obtained by carefully balancing the reconstruction loss and adversarial…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns…

This article presents a neural network approach for estimating the covariance function of spatial Gaussian random fields defined in a portion of the Euclidean plane. Our proposal builds upon recent contributions, expanding from the purely…

We present multi-point optimization: an optimization technique that allows to train several models simultaneously without the need to keep the parameters of each one individually. The proposed method is used for a thorough empirical…

Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural…

We consider a deep matrix factorization model of covariance matrices trained with the Bures-Wasserstein distance. While recent works have made advances in the study of the optimization problem for overparametrized low-rank matrix…

We study the generalization performance of unregularized gradient methods for separable linear classification. While previous work mostly deal with the binary case, we focus on the multiclass setting with $k$ classes and establish novel…

We derive an exact p-value for testing a global null hypothesis in a general adaptive regression problem. The general approach uses the Kac-Rice formula, as described in (Adler & Taylor 2007). The resulting formula is exact in finite…

We compute the distribution of triplets of stationary points in the energy landscape of the spherical p-spin model, by evaluating the quenched three-point complexity by means of the Kac-Rice formalism. We show the occurrence of transitions…

Joint modeling of spatially-oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes…

Statisticians often face the choice between using probability models or a paradigm defined by minimising a loss function. Both approaches are useful and, if the loss can be re-cast into a proper probability model, there are many tools to…

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…

Harnessing the local topography of the loss landscape is a central challenge in advanced optimization tasks. By accounting for the effect of potential parameter changes, we can alter the model more efficiently. Contrary to standard…

Building on the theory of causal discovery from observational data, we study interactions between multiple (sets of) random variables in a linear structural equation model with non-Gaussian error terms. We give a correspondence between…

This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…

Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…

Diffusion models are powerful generative models that produce high-quality samples from complex data. While their infinite-data behavior is well understood, their generalization with finite data remains less clear. Classical learning theory…

For a large class of feature maps we provide a tight asymptotic characterisation of the test error associated with learning the readout layer, in the high-dimensional limit where the input dimension, hidden layer widths, and number of…