相关论文: Convergence and Loss Bounds for Bayesian Sequence …
The Bayesian framework is ideally suited for induction problems. 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 distribution $\mu$ of the sequences…
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…
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 problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…
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…
We consider the Minimum Description Length principle for online sequence prediction. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure: (a) this quantity is…
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…
A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, one is required to give conditional probabilities of the next…
Solomonoff's uncomputable universal prediction scheme $\xi$ allows to predict the next symbol $x_k$ of a sequence $x_1...x_{k-1}$ for any Turing computable, but otherwise unknown, probabilistic environment $\mu$. This scheme will be…
The problem is that of sequential probability forecasting for finite-valued time series. The data is generated by an unknown probability distribution over the space of all one-way infinite sequences. It is known that this measure belongs to…
In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…
Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…
The problem of making sequential decisions in unknown probabilistic environments is studied. In cycle $t$ action $y_t$ results in perception $x_t$ and reward $r_t$, where all quantities in general may depend on the complete history. The…
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…
Construction methods for prior densities are investigated from a predictive viewpoint. Predictive densities for future observables are constructed by using observed data. The simultaneous distribution of future observables and observed data…
Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only…
Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…
In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data.…
We consider the problem of recovering a distribution function on the real line from observations additively contaminated with errors following the standard Laplace distribution. Assuming that the latent distribution is completely unknown…
Given a sequence $X=(X_1,X_2,\ldots)$ of random observations, a Bayesian forecaster aims to predict $X_{n+1}$ based on $(X_1,\ldots,X_n)$ for each $n\ge 0$. To this end, in principle, she only needs to select a collection…