Related papers: Criteria for the numerical constant recognition
We consider the quickest change detection problem where both the parameters of pre- and post- change distributions are unknown, which prevents the use of classical simple hypothesis testing. Without additional assumptions, optimal solutions…
We introduce a new nonparametric framework for classification problems in the presence of missing data. The key aspect of our framework is that the regression function decomposes into an anova-type sum of orthogonal functions, of which some…
Consider a collection of competing machine learning algorithms. Given their performance on a benchmark of datasets, we would like to identify the best performing algorithm. Specifically, which algorithm is most likely to rank highest on a…
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…
Symbolic regression, the task of predicting the mathematical expression of a function from the observation of its values, is a difficult task which usually involves a two-step procedure: predicting the "skeleton" of the expression up to the…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
Parametric prediction error methods constitute a classical approach to the identification of linear dynamic systems with excellent large-sample properties. A more recent regularized approach, inspired by machine learning and Bayesian…
Representation learning aims to extract meaningful lower-dimensional embeddings from data, known as representations. Despite its widespread application, there is no established definition of a ``good'' representation. Typically, the…
We study the best approximation problem: \[ \displaystyle \min_{\alpha\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m \alpha_j \Gamma_j ({\bf x}_i) \right|. \] Here: $\Gamma:=\left\{\Gamma_1,...,\Gamma_m\right\}$ is a list of…
We introduce a new criterion, the Rank Selection Criterion (RSC), for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models. The corresponding RSC estimator minimizes the Frobenius…
Automated scientific discovery aims to improve scientific understanding through machine learning. A central approach in this field is symbolic regression, which uses genetic programming or sparse regression to learn interpretable…
We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression…
We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…
The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…
Existing algorithms for subgroup discovery with numerical targets do not optimize the error or target variable dispersion of the groups they find. This often leads to unreliable or inconsistent statements about the data, rendering practical…
This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…
The continuation method is a popular approach in non-convex optimization and computer vision. The main idea is to start from a simple function that can be minimized efficiently, and gradually transform it to the more complicated original…