Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based

A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value

We consider the bias and variance of value function estimation that are caused by using an empirical model instead of the true model. We analyze these bias and variance for Markov processes from a classical (frequentist) statistical point of view, and in a Bayesian setting. Using a second

We consider a finite state, finite action, infinite horizon, discounted reward Markov Decision Process and study the bias and variance in the value function estimates that result from empirical estimates of the model parameters. We provide closed-form approximations for the bias and variance, which

\Ve compare sca.ling properties of severa.l value-function estimation algorithms. In particular, we prove that Q-learning can scale exponentially slowly with the number of states. \Ve identify the reasons of the slow convergence and show that both TD(..\) and learning with a fixed learning

This paper analyzes data on 11,600 students and their teachers who were randomly assigned to different size classes from kindergarten through third grade. Statistical methods are used to adjust for nonrandom attrition and transitions between classes. The main conclusions are (1) on average, performance on standardized tests increases by four percentile points the �rst year students attend small classes; (2) the test score advantage of students in small classes expands by about one percentile point per year in subsequent years; (3) teacher aides and measured teacher characteristics have little effect; (4) class size has a larger effect for minority students and those on free lunch; (5) Hawthorne effects were unlikely. I.

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considered estimation and inference for average treatment effects under weaker assumptions than typical of the earlier literature by avoiding distributional and functional-form assumptions. Various methods of semiparametric estimation have been proposed, including estimating the unknown regression functions

Motivation: Gene expression microarray experiments can generate data sets with multiple missing expression values. Unfortunately, many algorithms for gene expression analysis require a complete matrix of gene array values as input. For example, methods such as hierarchical clustering and K

In this paper we propose a new approach for constructing efficient schemes for nonsmooth convex optimization. It is based on a special smoothing technique, which can be applied to the functions with explicit max-structure. Our approach can be considered as an alternative to black-box minimization