Temat: empirical risk minimization

Skocz do pozycji: 1.

Tytuł:: On a dense minimizer of empirical risk in inverse problems
Autorzy:: Podlewski, J.
Szkutnik, Z.
Tematy:: inverse problem
empirical risk minimization; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/952841.pdf Link otwiera się w nowym oknie
Opis:: Properties of estimators of a functional parameter in an inverse problem setup are studied. We focus on estimators obtained through dense minimization (as opposed to minimization over δ-nets) of suitably defined empirical risk. At the cost of imposition of a sort of local finite-dimensionality assumption, we fill some gaps in the proofs of results published by Klemela and Mammen [Ann. Statist. 38 (2010), 482-511]. We also give examples of functional classes that satisfy the modified assumptions.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: A note on orthogonal series regression function estimators
Autorzy:: Popiński, Waldemar
Tematy:: consistent estimator
orthonormal system
empirical risk minimization
nonparametric regression; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Powiązania:: https://bibliotekanauki.pl/articles/1338775.pdf Link otwiera się w nowym oknie
Opis:: The problem of nonparametric estimation of the regression function f(x) = E(Y | X=x) using the orthonormal system of trigonometric functions or Legendre polynomials $e_k$, k=0,1,2,..., is considered in the case where a sample of i.i.d. copies $(X_i,Y_i)$, i=1,...,n, of the random variable (X,Y) is available and the marginal distribution of X has density ϱ ∈ $L^1$[a,b]. The constructed estimators are of the form $\widehat f_n(x) = \sum_{k=0}^{N(n)}\widehat c_ke_k(x)$, where the coefficients $\widehat c_0,\widehat c_1,...,\widehat c_N$ are determined by minimizing the empirical risk $n^{-1}\sum_{i=1}^n(Y_i - \sum_{k=0}^Nc_ke_k(X_i))^2$. Sufficient conditions for consistency of the estimators in the sense of the errors $E_X\vert f(X)-\widehat f_n(X)\vert^2$ and $n^{-1}\sum_{i=1}^nE(f(X_i)-\widehat f_n(X_i))^2$ are obtained.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Joint feature selection and classification for positive unlabelled multi-label data using weighted penalized empirical risk minimization
Autorzy:: Teisseyre, Paweł
Tematy:: positive data
unlabelled data
multilabel classification
feature selection
empirical risk minimization
dane pozytywne
dane nieoznaczone
klasyfikacja wieloetykietowa
selekcja cech; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Powiązania:: https://bibliotekanauki.pl/articles/2142491.pdf Link otwiera się w nowym oknie
Opis:: We consider the positive-unlabelled multi-label scenario in which multiple target variables are not observed directly. Instead, we observe surrogate variables indicating whether or not the target variables are labelled. The presence of a label means that the corresponding variable is positive. The absence of the label means that the variable can be either positive or negative. We analyze embedded feature selection methods based on two weighted penalized empirical risk minimization frameworks. In the first approach, we introduce weights of observations. The idea is to assign larger weights to observations for which there is a consistency between the values of the true target variable and the corresponding surrogate variable. In the second approach, we consider a weighted empirical risk function which corresponds to the risk function for the true unobserved target variables. The weights in both the methods depend on the unknown propensity score functions, whose estimation is a challenging problem. We propose to use very simple bounds for the propensity score, which leads to relatively simple forms of weights. In the experiments we analyze the predictive power of the methods considered for different labelling schemes.
Dostawca treści:: Biblioteka Nauki

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