Finite-Memory Universal Prediction of Individual Sequences

Meron, Eado; Feder, Meir

doi:10.1109/tit.2004.830749

Cited by 21 publications

(17 citation statements)

References 18 publications

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“…This framework we term resource bounded learning, and this is a very rich area in machine learning that needs to be explored both in a single task learning case and transfer learning case. Current work in this include Feder & Federovski, 1998;Rajwan & Feder, 2000;Meron & Feder, 2004. The results, particularly the last paper cited, are impressive.…”

Section: Future Workmentioning

confidence: 88%

On Universal Transfer Learning

Mahmud

2007

Lecture Notes in Computer Science

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The aim of transfer learning is to reduce sample complexity required to solve a learning task by using information gained from solving related tasks. Transfer learning has in general been motivated by the observation that when people solve problems, they almost always use information gained from solving related problems previously. Indeed, the thought of even children trying to solve problems tabula rasa seem absurd to us. Despite this fairly obvious observation, typical machine learning algorithms consider solving one task at a time and so do not take advantage of information that has become available from solving related tasks previously. Transfer methods aim to rectify this rather serious oversight and so have a potential to make a huge impact on how successful and widespread the use of machine learning is.Practical methods to transfer information has been developed and applied successfully to difficult real life problems. In addition theoretical analysis of these methods have been developed. However one fundamental problem still remains unsolved, which is how one measures similarity between tasks. This problem is obviously quite troubling from a conceptual point of view, as the notion of relatedness seem central to the objective of transferring information between related tasks. Furthermore, it has been shown in experiments that transferring from 'unrelated' tasks hurts generalization performance of learning algorithms. So an appropriate notion of similarity between tasks seem necessary to design algorithms that can determine when to transfer information, when not to and how much information to transfer. In this dissertation we give a formal solution to the problem of measuring task relatedness and all its associated problems.We derive a very general measure of relatedness between tasks. We show that this measure is universal -i.e. no other measure of relatedness can uncover much more similarity than our measure. We then use this measure to derive universally optimal transfer learning algorithms in a Bayesian setting. Universal optimality means that no other transfer learning algorithm can perform much better than ours.The methods we develop automatically solve the problems of determining when to transfer information and how much information to transfer. Indeed, we show ii that transferring information is always justified -i.e. it never hurts too much to transfer information. This latter result is quite surprising indeed as the commonly held belief in the transfer learning community is that it should hurt to transfer from unrelated tasks. We also show how our transfer learning methods may be used to do transfer in Prediction with Expert Advice Systems and in Reinforcement Learning agents as well.Our distance measures and learning algorithms are based on powerful, elegant and beautiful ideas from the field of Algorithmic Information Theory. While developing our transfer learning mechanisms we also derive results that are interesting in and of themselves. We also developed practical approximations to o...

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Section: Future Workmentioning

confidence: 88%

On Universal Transfer Learning

Mahmud

2007

Lecture Notes in Computer Science

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“…(As far as the symbol erased from window is unknown at every step, the number of symbols is recounted in accordance with a specific rule). We shall give an overview of such algorithms described in [2], [4] and [5].…”

Section: Data Compression Using "Sliding Window"mentioning

confidence: 99%

“…This algorithm is known as "Imaginary Sliding Window" (ISW). Feder and Meron in paper [4] gave an extensive review of estimation techniques using finite memory and suggested a method which consists of randomized finite-state machine replacement by time invariant deterministic finite-state machine (TIDFS). In this paper we suggest a way to implement derandomized method, which we shall call "virtual sliding window".…”

Section: Introductionmentioning

confidence: 99%

Binary Arithmetic Coding System with Adaptive Probability Estimation by "Virtual Sliding Window"

Belyaev

Gilmutdinov²,

Turlikov³

2006 IEEE International Symposium on Consumer Electronics

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Virtual Sliding Window" algorithm presented in this paper is an adaptive mechanism for estimating the probability of ones at the output of binary non-stationary sources. It is based on "Imaginary sliding window" idea proposed by B.Ryabko. The proposed algorithm was used as an alternative adaptation mechanism in Context-Based Adaptive Binary Arithmetic Coding (CABAC) -an entropy coding scheme of H.264/AVC standard for video compression. The "virtual sliding window" algorithm was integrated into an open-source codec supporting H.264/AVC standard. Comparison of the "virtual sliding window" algorithm with the original adaptation mechanism from CABAC is presented. Test results for standard video sequences are included. These results indicate that using the proposed algorithm improves rate-distortion performance compared to the original CABAC adaptation mechanism. Besides improvement in rate-distortion performances the "Virtual Sliding Window" algorithm has one more advantage. CABAC uses a finite state machine (FSM) for estimation of the probability of ones at the output of a binary source. Transitions for FSM are defined by a table stored in memory. The disadvantage of CABAC consists in frequent reference to this table (one time for every binary symbol encoding), which is critical for DSP implementation. The "Virtual Sliding Window" algorithm allows to avoid using the table of transitions 1 .

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“…In reality an implementation of probability smoothing has to work with finite precision arithmetic. Taking this into account [65] showed that a K-state FSM approximation of probability smoothing for a binary alphabet has re- Every state has N outgoing edges and an associated probability distribution. An outgoing edge (one for each letter) points to a follow-up state.…”

Section: Relative Frequencies With Smoothingmentioning

confidence: 99%

“…Any K-state FSM predictor has redundancy at least Θ(K −4/5 · n) [65]. Later, this lower bound was improved [44] and the authors proposed an FSM con-struction algorithm: Given per-bit redundancy R, the algorithm constructs an FSM with per-bit redundancy close to R. Other approaches rely on randomization, the FSM proposed in [66] simulates an Imaginary Sliding Window (see next section) and attains expected redundancy O(…”

Section: Relative Frequencies With Smoothingmentioning

confidence: 99%

Statistical Data Compression

Mattern¹

SpringerReference

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The ongoing evolution of hardware leads to a steady increase in the amount of data that is processed, transmitted and stored. Data compression is an essential tool to keep the amount of data manageable. Furthermore, techniques from data compression have many more applications beyond compression, for instance data clustering, classification and time series prediction.In terms of empirical performance statistical data compression algorithms rank among the best. A statistical data compressor processes an input text letter by letter and performs compression in two stages -modeling and coding. During modeling a model estimates a probability distribution on the next letter based on the past input. During coding an encoder translates this probability distribution and the next letter into a codeword. Decoding reverts this process. Note that the model is exchangeable and its actual choice determines a statistical data compression algorithm. All major models use a mixer to combine multiple simple probability estimators, so-called elementary models.In statistical data compression there is an increasing gap between theory and practice. On the one hand, the "theoretician's approach" puts emphasis on models that allow for a mathematical code length analysis to evaluate their performance, but neglects running time and space considerations and empirical improvements. On the other hand the "practitioner's approach" focuses on the very reverse. The family of PAQ statistical compressors demonstrated the superiority of the "practitioner's approach" in terms of empirical compression rates.With this thesis we attempt to bridge the aforementioned gap between theory and practice with special focus on PAQ. To achieve this we apply the theoretician's tools to practitioner's approaches: We provide a code length analysis for several common and practical modeling and mixing techniques. The analysis covers modeling by relative frequencies with frequency discount and modeling by exponential smoothing of probabilities. For mixing we consider linear and geometrically weighted averaging of probabilities with Online Gradient Descent for weight estimation. Our results show that the models and mixers we consider perform nearly as well as idealized competitors that may adapt to the input. Experiments support our analysis. Moreover, our results add a theoretical justification to modeling and mixing from PAQ and generalize methods from PAQ. ii

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Finite-Memory Universal Prediction of Individual Sequences

Cited by 21 publications

References 18 publications

On Universal Transfer Learning

On Universal Transfer Learning

Binary Arithmetic Coding System with Adaptive Probability Estimation by "Virtual Sliding Window"

Statistical Data Compression

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