Related papers: On optimal linear prediction
Quantum computers can be considered as a natural means for performing machine learning tasks for inherently quantum labeled data. Many quantum machine learning techniques have been developed for solving classification problems, such as…
A set of probabilistic predictions is well calibrated if the events that are predicted to occur with probability p do in fact occur about p fraction of the time. Well calibrated predictions are particularly important when machine learning…
As quantum tomography is becoming a key component of the quantum engineering toolbox, there is a need for a deeper understanding of the multitude of estimation methods available. Here we investigate and compare several such methods: maximum…
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…
We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…
This paper presents a new approach to distributed linear filtering and prediction. The problem under consideration consists of a random dynamical system observed by a multi-agent network of sensors where the network is sparse. Inspired by…
Improving algorithms via predictions is a very active research topic in recent years. This paper initiates the systematic study of mechanism design in this model. In a number of well-studied mechanism design settings, we make use of…
We introduce algorithms that use predictions from machine learning applied to the input to circumvent worst-case analysis. We aim for algorithms that have near optimal performance when these predictions are good, but recover the…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
The problem of astrometry is revisited from the perspective of analyzing the attainability of well-known performance limits (the Cramer-Rao bound) for the estimation of the relative position of light-emitting (usually point-like) sources on…
We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of density operators. We show that the design…
We obtain robust and computationally efficient estimators for learning several linear models that achieve statistically optimal convergence rate under minimal distributional assumptions. Concretely, we assume our data is drawn from a…
Machine learning is often used in competitive scenarios: Participants learn and fit static models, and those models compete in a shared platform. The common assumption is that in order to win a competition one has to have the best…
Subsampling is commonly used to overcome computational and economical bottlenecks in the analysis of finite populations and massive datasets. Existing methods are often limited in scope and use optimality criteria (e.g., A-optimality) with…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
Stacking regressions is an ensemble technique that forms linear combinations of different regression estimators to enhance predictive accuracy. The conventional approach uses cross-validation data to generate predictions from the…
The least squares fit to a straight line, when both variables are affected by all equal uncorrelated errors, leads to very simple results for both the estimated parameters and their standard errors, of widespread applicability. In this…
When is optimal estimation linear? It is well known that, when a Gaussian source is contaminated with Gaussian noise, a linear estimator minimizes the mean square estimation error. This paper analyzes, more generally, the conditions for…
Data-driven, machine learning (ML) models of atomistic interactions are often based on flexible and non-physical functions that can relate nuanced aspects of atomic arrangements into predictions of energies and forces. As a result, these…
Conformal predictors provide set or functional predictions that are valid under the assumption of randomness, i.e., under the assumption of independent and identically distributed data. The question asked in this paper is whether there are…