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 enough to include cases in which no minimum exists, as occurs typically, for instance, with standard boosting algorithms. Concretely, we first show that any...

Empirical evidence shows that entrepreneurs hold a large fraction of wealth, have higher saving rates than workers, and face substantial uninsurable entrepreneurial and investment risks. This paper constructs a heterogeneous-agent general equilibrium model with uninsurable entrepreneurial risk and capital-market imperfections to explore the implications of uninsurable entrepreneurial risk for w...

Let (X ,μ) be a probability space, set X to be distributed according to μ and put Y to be an unknown target random variable. In the usual setup in learning theory, one observes N independent couples (Xi, Yi)Ni=1 in X × R, distributed according to the joint distribution of X and Y . The goal is to construct a real-valued function f which is a good guess/prediction of Y . A standard way of measur...

return maximization or risk minimization is goal in portfolio optimization based on mean variance theory. the structure of correlation matrices and individual variance of each asset are two main factors in optimization with risk minimization object. it’s necessary to use appropriate variance and correlation coefficient for time series with clustering volatilities feature, too. in this research,...

Methodological norms in economic theorising are interpreted as rational strategies to optimise some epistemic utility functions. A definition of ‘empirical verisimilitude’ is defended as a plausible interpretation of the epistemic preferences of researchers. Some salient differences between the scientific strategies of physics and of economics are derived from the comparison of the relative cos...

A generic fusion problem is studied for multiple sensors whose outputs are probabilistically related to their inputs according to unknown distributions. Sensor measurements are provided as iid input-output samples, and an empirical risk minimization method is described for designing fusers with distribution-free performance bounds. The special cases of isolation and projective fusers for classi...

In this paper, we study a two-category classification problem. We indicate the categories by labels Y = 1 and Y = −1. We observe a covariate, or feature, X ∈ X ⊂ R. Consider a collection {ha} of classifiers indexed by a finite-dimensional parameter a, and the classifier ha∗ that minimizes the prediction error over this class. The parameter a∗ is estimated by the empirical risk minimizer ân over...

We address the problem of sequential prediction in the heteroscedastic setting, when both the signal and its variance are assumed to depend on explanatory variables. By applying regret minimization techniques, we devise an efficient online learning algorithm for the problem, without assuming that the error terms comply with a specific distribution. We show that our algorithm can be adjusted to ...

We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error (MAE) regression. We show that universal consistency of Empirical Risk Minimization remains possible using the MAPE instead of the MAE.

Support Vector Machine (SVM) is a classification technique based on Structural Risk Minimization (SRM), which can run on MATLAB. For classification of nonseparable samples, conventional SVM needs to select a tradeoff between maximization the margin and misclassification rate. In order to guarantee generalized performance and low misclassification rate of SVM, this paper puts forward an improved...