Related papers: On optimal linear prediction
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…
In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal…
We propose a numerical algorithm for finding optimal measurements for quantum-state discrimination. The theory of the semidefinite programming provides a simple check of the optimality of the numerically obtained results.
We study the least square estimator, in the framework of simple linear regression, when the deviance term $\varepsilon$ with respect to the linear model is modeled by a uniform distribution. In particular, we give the law of this estimator,…
Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the…
Neural predictive models have achieved remarkable performance improvements in various natural language processing tasks. However, most neural predictive models suffer from the lack of explainability of predictions, limiting their practical…
In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…
Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…
Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…
The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…
The estimation of parameters from data is a common problem in many areas of the physical sciences, and frequently used algorithms rely on sets of simulated data which are fit to data. In this article, an analytic solution for…
Recent works have proposed various explanations for the ability of modern large language models (LLMs) to perform in-context prediction. We propose an alternative conceptual viewpoint from an information-geometric and statistical…
In this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields…
We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
To find efficient screening methods for high dimensional linear regression models, this paper studies the relationship between model fitting and screening performance. Under a sparsity assumption, we show that a subset that includes the…
Overparametrization often helps improve the generalization performance. This paper presents a dual view of overparametrization suggesting that downsampling may also help generalize. Focusing on the proportional regime $m\asymp n \asymp p$,…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…