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We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and…
Decoding, ie prediction from brain images or signals, calls for empirical evaluation of its predictive power. Such evaluation is achieved via cross-validation, a method also used to tune decoders' hyper-parameters. This paper is a review on…
This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant…
We explore the performance of several automatic bandwidth selectors, originally designed for density gradient estimation, as data-based procedures for nonparametric, modal clustering. The key tool to obtain a clustering from density…
Quantum computing algorithms have been shown to produce performant quantum kernels for machine-learning classification problems. Here, we examine the performance of quantum kernels for regression problems of practical interest. For an…
When selecting a classification algorithm to be applied to a particular problem, one has to simultaneously select the best algorithm for that dataset \emph{and} the best set of hyperparameters for the chosen model. The usual approach is to…
Allthough nonparametric kernel density estimation with bias reduce is nowadays a standard technique in explorative data-analysis, there is still a big dispute on how to assess the quality of the estimate and which choice of bandwidth is…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
This paper presents a new insight into improving the performance of Stochastic Neighbour Embedding (t-SNE) by using Isolation kernel instead of Gaussian kernel. Isolation kernel outperforms Gaussian kernel in two aspects. First, the use of…
Cross-validation is a useful and generally applicable technique often employed in machine learning, including decision tree induction. An important disadvantage of straightforward implementation of the technique is its computational…
This text is a survey on cross-validation. We define all classical cross-validation procedures, and we study their properties for two different goals: estimating the risk of a given estimator, and selecting the best estimator among a given…
We consider estimating the density of a response conditioning on an error-prone covariate. Motivated by two existing kernel density estimators in the absence of covariate measurement error, we propose a method to correct the existing…
In this paper, we consider derivative free optimization problems, where the objective function is smooth but is computed with some amount of noise, the function evaluations are expensive and no derivative information is available. We are…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…
This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…
Continuous treatments (e.g., doses) arise often in practice, but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowing doubly robust covariate adjustment. We…
Hard-threshold estimators are popular in signal processing applications. We provide a detailed study of using hard-threshold estimators for estimating an unknown deterministic signal when additive white Gaussian noise corrupts observations.…
Nonparametric estimation of copula density functions using kernel estimators presents significant challenges. One issue is the potential unboundedness of certain copula density functions at the corners of the unit square. Another is the…