Fedor Zhdanov

Prediction with expert advice under discounted loss

We study prediction with expert advice in the setting where the losses are accumulated with some discounting and the impact of old losses can gradually vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm for Regression, propose a new variant of exponentially weighted average algorithm, and prove bounds on the cumulative discounted loss.

Prediction with expert advice for the Brier game

We show that the Brier game of prediction is mixable and find the optimal learning rate and substitution function for it. The resulting prediction algorithm is applied to predict results of football and tennis matches. The theoretical performance guarantee turns out to be rather tight on these data sets, especially in the case of the more extensive tennis data.

An identity for kernel ridge regression

This paper derives an identity connecting the square loss of ridge regression in on-line mode with the loss of the retrospectively best regressor. Some corollaries about the properties of the cumulative loss of on-line ridge regression are also obtained.

Supermartingales in Prediction with Expert Advice

This paper compares two methods of prediction with expert advice, the Aggregating Algorithm and the Defensive Forecasting, in two different settings. The first setting is traditional, with a countable number of experts and a finite number of outcomes. Surprisingly, these two methods of fundamentally different origin lead to identical procedures. In the second setting the experts can give advice conditional on the learners future decision. Both methods can be used in the new setting and give the same performance guarantees as in the traditional setting. However, whereas defensive forecasting can be applied directly, the AA requires substantial modifications.

Online Prediction of Ovarian Cancer

In this paper we apply computer learning methods to the diagnosis of ovarian cancer using the level of the standard biomarker CA125 in conjunction with information provided by mass spectrometry. Our algorithm gives probability predictions for the disease. To check the power of our algorithm we use it to test the hypothesis that CA125 and the peaks do not contain useful information for the prediction of the disease at a particular time before the diagnosis. It produces p -values that are less than those produced by an algorithm that has been previously applied to this data set. Our conclusion is that the proposed algorithm is especially reliable for prediction the ovarian cancer on some stages.

Linear Probability Forecasting

In this paper we consider two online multi-class classification problems: classification with linear models and with kernelized models. The predictions can be thought of as probability distributions. The quality of predictions is measured by the Brier loss function. We suggest two computationally efficient algorithms to work with these problems, the second algorithm is derived by considering a new class of linear prediction models. We prove theoretical guarantees on the cumulative losses of the algorithms. We kernelize one of the algorithms and prove theoretical guarantees on the loss of the kernelized version. We perform experiments and compare our algorithms with logistic regression.

UNIVERSAL ALGORITHMS FOR PROBABILITY FORECASTING

Multi-class classification is one of the most important tasks in machine learning. In this paper we consider two online multi-class classification problems: classification by a linear model and by a kernelized model. The quality of predictions is measured by the Brier loss function. We obtain two computationally efficient algorithms for these problems by applying the Aggregating Algorithms to certain pools of experts and prove theoretical guarantees on the losses of these algorithms. We kernelize one of the algorithms and prove theoretical guarantees on its loss. We perform experiments and compare our algorithms with logistic regression.