We present an algorithm based on statistical learning for synthesizing static and time-varying textures matching the appearance of an input texture. Our algorithm is general and automatic, and it works well on various types of textures including 1D sound textures, 2D texture images and 3D texture movies. The same method is also used to generate 2D texture mixtures that simultaneously capture the appearance of a number of different input textures. In our approach, input textures are treated as sample signals generated by a stochastic process. We first construct a tree representing a hierarchical multi-scale transform of the signal using wavelets. From this tree, new random trees are generated by learning and sampling the conditional probabilities of the paths in the original tree. Transformation of these random trees back into signals results in new random textures. In the case of 2D texture synthesis our algorithm produces results that are generally as good or better than those produce...

A discrete denoising algorithm estimates the input sequence to a discrete memoryless channel (DMC) based on the observation of the entire output sequence. For the case in which the DMC is known and the quality of the reconstruction is evaluated with a given single-letter fidelity criterion, we propose a discrete denoising algorithm that does not assume knowledge of statistical properties of the input sequence. Yet, the algorithm is universal in the sense of asymptotically performing as well as the optimum denoiser that knows the input sequence distribution, which is only assumed to be stationary and ergodic. Moreover, the algorithm is universal also in a semi-stochastic setting, in which the input is an individual sequence, and the randomness is due solely to the channel noise.

We show that the Hausdorff dimension equals the logarithmic loss unpredictability for any set of infinite sequences over a finite alphabet. Using computable, feasible, and finite-state predictors, this equivalence also holds for the recently introduced computable, feasible, and finite-state dimensions [Lutz (2000) and Dai, Lathrop, Lutz, and Mayordomo (2001)]. Combining this with recent results of Fortnow and Lutz (2002), we have a tight relationship between prediction with respect to logarithmic loss and absolute loss.

Abstract not found

One objective of artificial intelligence is to model the behavior of an intelligent agent interacting with its environment. The environment's transformations could be modeled as a Markov chain, whose state is partially observable to the agent and affected by its actions; such processes are known as partially observable Markov decision processes (POMDPs). While the environment's dynamics are assumed to obey certain rules, the agent does not know them and must learn. In this dissertation we focus on the agent's adaptation as captured by the reinforcement learning framework. Reinforcement learning means learning a policy---a mapping of observations into actions---based on feedback from the environment. The learning can be viewed as browsing a set of policies while evaluating them by trial through interaction with the environment. The set of policies being searched is constrained by the architecture of the agent's controller. POMDPs require a controller to have a memory. We investigate various architectures for controllers with memory, including controllers with external memory, finite state controllers and distributed controllers for multi-agent system. For these various controllers we work out the details of the algorithms which learn by ascending the gradient of expected cumulative reinforcement. Building on statistical learning theory and experiment design theory, a policy evaluation algorithm is developed for the case of experience re-use. We address the question of sufficient experience for uniform convergence of policy evaluation and obtain sample complexity bounds for various estimators. Finally, we demonstrate the performance of the proposed algorithms on several domains, the most complex of which is simulated adaptive packet routing in a telecommunication network.

Abstract not found

We consider repeated games in which the player, instead of observing the action chosen by the opponent in each game round, receives a feedback generated by the combined choice of the two players. We study Hannan consistent players for this games; that is, randomized playing strategies whose per-round regret vanishes with probability one as the number n of game rounds goes to infinity. We prove a general lower bound of Ω(n^−1/3) on the convergence rate of the regret, and exhibit a specific strategy that attains this rate on any game for which a Hannan consistent player exists.

The probability of observing $x_t$ at time $t$, given past observations $x_1...x_{t-1}$ can be computed with Bayes rule if the true generating distribution $\mu$ of the sequences $x_1x_2x_3...$ is known. If $\mu$ is unknown, but known to belong to a class $M$ one can base ones prediction on the Bayes mix $\xi$ defined as a weighted sum of distributions $ u\in M$. Various convergence results of the mixture posterior $\xi_t$ to the true posterior $\mu_t$ are presented. In particular a new (elementary) derivation of the convergence $\xi_t/\mu_t\to 1$ is provided, which additionally gives the rate of convergence. A general sequence predictor is allowed to choose an action $y_t$ based on $x_1...x_{t-1}$ and receives loss $\ell_{x_t y_t}$ if $x_t$ is the next symbol of the sequence. No assumptions are made on the structure of $\ell$ (apart from being bounded) and $M$. The Bayes-optimal prediction scheme $\Lambda_\xi$ based on mixture $\xi$ and the Bayes-optimal informed prediction scheme $\Lambda_\mu$ are defined and the total loss $L_\xi$ of $\Lambda_\xi$ is bounded in terms of the total loss $L_\mu$ of $\Lambda_\mu$. It is shown that $L_\xi$ is bounded for bounded $L_\mu$ and $L_\xi/L_\mu\to 1$ for $L_\mu\to \infty$. Convergence of the instantaneous losses is also proven.

Sequential randomized prediction of an arbitrary binary sequence is investigated.

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 statistical guidelines for choosing the model class and prior are not always available or can fail, in particular in complex situations. Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. I discuss in breadth how and in which sense universal (non-i.i.d.) sequence prediction solves various (philosophical) problems of traditional Bayesian sequence prediction. I show that Solomonoff’s model possesses many desirable properties: Strong total and future bounds, and weak instantaneous bounds, and in contrast to most classical continuous prior densities has no zero p(oste)rior problem, i.e. can confirm universal hypotheses, is reparametrization and regrouping invariant, and avoids the old-evidence and updating problem. It even performs well