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Iterative ridge regression using the aggregating algorithm *

PATTERN RECOGNITION LETTERS 2022年 158卷 34-41页

作者： Jamil, Waqas Bouchachia, Abdelhamid Bournemouth Univ Dept Comp & Informat Poole BH12 5BB England

In this paper, regularised regression for sequential data is investigated and a new ridge regression algo-rithm is proposed. It uses the aggregating algorithm (AA) to devise an iterative version of ridge regression (IRR). This algorithm is called AAIRR. A competitive analysis is conducted to show that the guarantee on the performance of AAIRR is better than that of the known online ridge regression algorithms. Moreover, an empirical study is carried out on real-world datasets to demonstrate the superior performance over those state-of-the-art algorithms.(c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://***/licenses/by/4.0/ )

关键词： Online machine learning Ridge regression aggregating algorithm Online machine learning Ridge regression aggregating algorithm

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Practical investment with the long-short game

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ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE 2023年 1-32页

作者： Al-baghdadi, Najim Kalnishkan, Yuri Lindsay, David Lindsay, Sian Univ London Royal Holloway Dept Comp Sci Egham Hill Egham TW20 0EX Surrey England AlgoLabs Ocean House Bracknell RG12 1AX Berkshire England

In this paper we apply methods of prediction with expert advice to real-world foreign exchange trading data with the aim of finding effective investment strategies. We start with the framework of the long-short game, introduced by Vovk and Watkins (1998), and then propose modifications aimed at improving the performance with respect to standard portfolio performance indicators.

关键词： Prediction with expert advice Online learning aggregating algorithm Portfolio optimisation Long-short game Foreign exchange Currency trading

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Anomaly detection with superexperts under delayed feedback

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ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE 2023年 1-30页

作者： Dzhamtyrova, Raisa Maple, Carsten Univ London Ctr Reliable Machine Learning London England Univ London Dept Comp Sci Royal Holloway London England Univ Warwick Alan Turing Inst Warwick England Univ Warwick WMG Cyber Secur Ctr Warwick England

The increasing connectivity of data and cyber-physical systems has resulted in a growing number of cyber-attacks. Real-time detection of such attacks, through the identification of anomalous activity, is required so that mitigation and contingent actions can be effectively and rapidly deployed. We propose a new approach for aggregating unsupervised anomaly detection algorithms incorporating feedback when it becomes available. We apply this approach to open-source real datasets and show that both aggregating models, which we call experts, and incorporating feedback significantly improve performance. An important property of the proposed approaches is their theoretical guarantees that they perform close to the best superexpert, which can switch between the best performing experts, in terms of the cumulative average losses.

关键词： Anomaly detection Online learning Prediction with expert advice aggregating algorithm

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Online Aggregation of Conformal Forecasting Systems

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JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS 2023年第SUPPL 2期68卷 S239-S253页

作者： V'yugin, V. V. Trunov, V. G. Russian Acad Sci Kharkevich Inst Informat Transmiss Problems Moscow 127051 Russia

The problem of online probabilistic time series forecasting is considered. Probabilistic forecasts are obtained as a result of the application of conformal forecasting systems. The conformal forecasting system is defined on the basis of point forecasts of the regression algorithm. The corresponding probability distribution function is used to assess the degree of reliability of the algorithm's predictions. The paper considers the case when at each moment of time several competing methods (experts) present their forecasts in the form of distribution functions. These distributions are constructed online from point predictions using the conformal prediction method. The probabilistic forecasts of experts are combined using an aggregating algorithm into one probabilistic forecast at each stage of the forecasting process, while expert forecasts can be used at a discount. A technology has been developed for constructing predictive expert algorithms and aggregation of their probabilistic forecasts on the example of the problem of forecasting the hourly load of an electric network depending on the temperature forecast. The results of numerical experiments on real data are presented;a comparative analysis of the method of conformal predictions and the method of Gaussian mixtures is carried out.

关键词： machine learning online probabilistic forecasting conformal forecasting systems forecast calibration prediction with expert advice regret confidence levels aggregating algorithm continuous ranked probability score (CRPS) CRPS forecasting in an electric network

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The geometry and calculus of losses

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2023年第1期24卷 16341-16412页

作者： Robert C. Williamson Zac Cranko University of Tübingen and Tübingen AI Center Germany Sydney Australia

Statistical decision problems lie at the heart of statistical machine learning. The simplest problems are multiclass classification and class probability estimation. Central to their definition is the choice of loss function, which is the means by which the quality of a solution is evaluated. In this paper we systematically develop the theory of loss functions for such problems from a novel perspective whose basic ingredients are convex sets with a particular structure. The loss function is defined as the subgradient of the support function of the convex set. It is consequently automatically proper (calibrated for probability estimation). This perspective provides three novel opportunities. It enables the development of a fundamental relationship between losses and (anti)-norms that appears to have not been noticed before. Second, it enables the development of a calculus of losses induced by the calculus of convex sets which allows the interpolation between different losses, and thus is a potential useful design tool for tailoring losses to particular problems. In doing this we build upon, and considerably extend, existing results on M-sums of convex sets. Third, the perspective leads to a natural theory of "polar" loss functions, which are derived from the polar dual of the convex set defining the loss, and which form a natural universal substitution function for Vovk's aggregating algorithm.

关键词： convex sets support functions gauges polars concave duality proper loss functions M-sums distorted probabilities polar losses Shephard duality anti-norms Bregman divergences semi inner products Finsler geometry aggregating algorithm substitution functions direct and inverse addition

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Online aggregation of probability forecasts with confidence

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PATTERN RECOGNITION 2022年 121卷 108193-108193页

作者： V'yugin, Vladimir Trunov, Vladimir Russian Acad Sci Inst Informat Transmiss Problems Bolshoi Karetnyi Per 19GSP 4 Moscow 127994 Russia

The paper presents numerical experiments and some theoretical developments in prediction with expert advice (PEA). One experiment deals with predicting electricity consumption depending on temperature and uses real data. As the pattern of dependence can change with season and time of the day, the domain naturally admits PEA formulation with experts having different "areas of expertise". We consider the case where several competing methods produce online predictions in the form of probability distribution functions. The dissimilarity between a probability forecast and an outcome is measured by a loss function (scoring rule). A popular example of scoring rule for continuous outcomes is Continuous Ranked Probability Score ( CRPS ). In this paper the problem of combining probabilistic forecasts is considered in the PEA framework. We show that CRPS is a mixable loss function and then the time-independent upper bound for the regret of the Vovk aggregating algorithm using CRPS as a loss function can be obtained. Also, we incorporate a "smooth" version of the method of specialized experts in this scheme which allows us to combine the probabilistic predictions of the specialized experts with overlapping domains of their competence. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： On-line learning Prediction with expert advice aggregating algorithm Probabilistic prediction Smooth confidence levels for experts

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Online Aggregation of Probabilistic Forecasts Based on the Continuous Ranked Probability Score

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JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS 2020年第6期65卷 662-676页

作者： V'yugin, V. V. Trunov, V. G. Kharkevich Inst Informat Transmiss Problems Moscow 127051 Russia

Methods for generating predictions online and in the form of probability distributions of future outcomes are considered. The difference between the probabilistic forecast (probability distribution) and the numerical outcome is measured using the loss function (scoring rule). In practical statistics, the continuous ranked probability score (CRPS) is often used to estimate the discrepancy between probabilistic forecasts and (quantitative) outcomes. The paper considers the case when several competing methods (experts) give their online predictions as distribution functions. An algorithm is proposed for online aggregation of these distribution functions. The performance bounds of the proposed algorithm are obtained in the form of a comparison of the cumulative loss of the algorithm and the loss of expert hypotheses. Unlike existing estimates, the proposed estimates do not depend on time. The results of numerical experiments illustrating the proposed methods are presented.

关键词： prediction with expert advice online decision making regret aggregating algorithm continuous ranked probability score (CRPS) mixable loss function

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Mixing Past Predictions 9

Mixing Past Predictions

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9th Symposium on Conformal and Probabilistic Predictions with Applications (COPA)

作者： Korotin, Alexander V'yugin, Vladimir Burnaev, Evgeny Skolkovo Inst Sci & Technol Moscow Russia Inst Informat Transmiss Problems Moscow Russia

In the framework of the theory of prediction with expert advice, we present an algorithm for online aggregation of the functional predictions. The approach implies that at each time step some algorithm issues a forecast in the form of a function and then the master algorithm combines these current and past functional forecasts into one aggregated functional forecast. We apply the proposed algorithm for the problem of long-term predictions of time series. By combining the past and current long-term functional forecasts, we obtain a smoothing mechanism that protects our algorithm from temporary changes in the trend of time series, noise and outliers. To evaluate the performance of presented aggregating algorithm as a long-term forecaster we use a new "integral" loss function and the delayed feedback approach. We apply this algorithm for the regression problems, we present some method for smoothing regression forecasts.

关键词： Functional forecasts Integral loss function Mixable loss function aggregating algorithm Long-term online forecasting Prediction with expert advice Online smoothing regression

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Practical Investment with the Long-Short Game 9

Practical Investment with the Long-Short Game

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9th Symposium on Conformal and Probabilistic Predictions with Applications (COPA)

作者： Al-baghdadi, Najim Kalnishkan, Yuri Lindsay, David Lindsay, Sian Royal Holloway Univ London Dept Comp Sci Egham Surrey England Moscow Inst Phys & Technol Lab Adv Combinator & Network Applicat Inst Sky Per 9 Dolgoprudnyi 41701 Russia AlgoLabs Bracknell Berks England

In this paper we apply the aggregating algorithm, an on-line prediction with expert advice algorithm, to real-world foreign exchange trading data with the aim of finding investment strategies with optimal returns. We consider the Long-Short game first introduced in Vovk and Watkins (1998) and it's implementation, including the derivation of expert predictions from model trading data. Furthermore, we propose modifications to improve the practical performance of the game with respect to well-known portfolio performance indicators.

关键词： Prediction with Expert Advice Online Learning aggregating algorithm Portfolio Optimisation Long-Short Game Foreign Exchange Currency Trading

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Competitive Online Regression under Continuous Ranked Probability Score 8

Competitive Online Regression under Continuous Ranked Probab...

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8th Symposium on Conformal and Probabilistic Predictions with Applications (COPA)

作者： Dzhamtyrova, Raisa Kalnishkan, Yuri Royal Holloway Univ London Dept Comp Sci Egham Surrey England Moscow Inst Phys & Technol Lab Adv Combinator & Network Applicat Egham Surrey England

We consider the framework of competitive prediction when one provides guarantees compared to other predictive models that are called experts. We propose the algorithm that combines point predictions of an infinite pool of linear experts and outputs probability forecasts in the form of cumulative distribution functions. We evaluate the quality of probabilistic prediction by the continuous ranked probability score (CRPS), which is a widely used proper scoring rule. We provide a strategy that allows us to 'track the best expert' and derive the theoretical bound on the discounted loss of the strategy. Experimental results on synthetic data and solar power data show that the theoretical bounds of our algorithm are not violated. Also the algorithm performs close to and sometimes outperforms the retrospectively best quantile regression.

关键词： prediction with expert advice online learning competitive prediction aggregating algorithm continuous ranked probability score (CRPS) probabilistic forecasting

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