相关论文: Sequence Prediction based on Monotone Complexity

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…

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…

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.…

The problem of sequential probability forecasting is considered in the most general setting: a model set C is given, and it is required to predict as well as possible if any of the measures (environments) in C is chosen to generate the…

The paper established sufficient conditions of predictability with degeneracy for the spectrum at $M$-periodically located isolated points on the unit circle. It is also shown that $m$-periodic subsequences of these sequences are also…

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…

A selection of the relevant theorems of Probability Theory that comes directly from Kolmogorov's axioms, Set Theory basic results, definitions and rules of inference are listed and proven in a systematic approach, aiming the student who…

Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…

Stochastic approximation (SA) that involves multiple coupled sequences, known as multiple-sequence SA (MSSA), finds diverse applications in the fields of signal processing and machine learning. However, existing theoretical understandings…

The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…

A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new ``normalized information distance'', based on the noncomputable notion of…

Since the introduction of the Kolmogorov complexity of binary sequences in the 1960s, there have been significant advancements in the topic of complexity measures for randomness assessment, which are of fundamental importance in theoretical…

The linear complexity (LC) of a sequence has been used as a convenient measure of the randomness of a sequence. Based on the theories of linear complexity, $k$-error linear complexity, the minimum error and the $k$-error linear complexity…

Autonomous systems with machine learning-based perception can exhibit unpredictable behaviors that are difficult to quantify, let alone verify. Such behaviors are convenient to capture in probabilistic models, but probabilistic model…

In this work we establish the posterior consistency for a parametrized family of partially observed, fully dominated Markov models. As a main assumption, we suppose that the prior distribution assigns positive probability to all…

We consider generalized solutions of the Perona-Malik equation in dimension one, defined as all possible limits of solutions to the semi-discrete approximation in which derivatives with respect to the space variable are replaced by…

We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known…

The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…

In this paper, we solve the problem of predicting the next locations of the moving objects with a historical dataset of trajectories. We present a Next Location Predictor with Markov Modeling (NLPMM) which has the following advantages: (1)…

We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a "penalized divergence" of the prior, which measures the ability of the prior distribution to propose a nonnegligible…