相关论文: Sequential Predictions based on Algorithmic Comple…

We construct universal prediction systems in the spirit of Popper's falsifiability and Kolmogorov complexity and randomness. These prediction systems do not depend on any statistical assumptions (but under the IID assumption they dominate,…

The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms…

This paper establishes for the first time the predictive performance of speed priors and their computational complexity. A speed prior is essentially a probability distribution that puts low probability on strings that are not efficiently…

Solomonoff sequence prediction is a scheme to predict digits of binary strings without knowing the underlying probability distribution. We call a prediction scheme informed when it knows the true probability distribution of the sequence.…

Compression and generalization are fundamentally related through Solomonoff induction and the minimum description length principle (MDL), which predict that simpler models generalize better when data arises from low-complexity…

The Bayesian framework is a well-studied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard…

We study algorithmic randomness and monotone complexity on product of the set of infinite binary sequences. We explore the following problems: monotone complexity on product space, Lambalgen's theorem for correlated probability,…

Recent developments have linked causal inference with Algorithmic Information Theory, and methods have been developed that utilize Conditional Kolmogorov Complexity to determine causation between two random variables. We present a method…

Many learning tasks can be viewed as sequence prediction problems. For example, online classification can be converted to sequence prediction with the sequence being pairs of input/target data and where the goal is to correctly predict the…

The coding theorem for Kolmogorov complexity states that any string sampled from a computable distribution has a description length close to its information content. A coding theorem for resource-bounded Kolmogorov complexity is the key to…

The property of learning-curve monotonicity, highlighted in a recent series of work by Loog, Mey and Viering, describes algorithms which only improve in average performance given more data, for any underlying data distribution within a…

Machine learning (ML) models for molecules and materials commonly rely on a decomposition of the global target quantity into local, atom-centered contributions. This approach is convenient from a computational perspective, enabling…

Various optimality properties of universal sequence predictors based on Bayes-mixtures in general, and Solomonoff's prediction scheme in particular, will be studied. The probability of observing $x_t$ at time $t$, given past observations…

Solomonoff's inductive learning model is a powerful, universal and highly elegant theory of sequence prediction. Its critical flaw is that it is incomputable and thus cannot be used in practice. It is sometimes suggested that it may still…

We summarize our recent findings, where we proposed a framework for learning a Kolmogorov model, for a collection of binary random variables. More specifically, we derive conditions that link outcomes of specific random variables, and…

Partially Observable Markov Decision Processes (POMDPs) model decision making under uncertainty. While there are many approaches to approximately solving POMDPs, we aim to address the problem of learning such models. In particular, we are…

Sequential probability assignment and universal compression go hand in hand. We propose sequential probability assignment for non-binary (and large alphabet) sequences with empirical distributions whose parameters are known to be bounded…

This paper is concerned with algorithms for prediction of discrete sequences over a finite alphabet, using variable order Markov models. The class of such algorithms is large and in principle includes any lossless compression algorithm. We…

The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting…

This chapter discusses the Solomonoff approach to universal prediction. The crucial ingredient in the approach is the notion of computability, and I present the main idea as an attempt to meet two plausible computability desiderata for a…