Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible

We propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test. By using probabilistic transition systems as the underlying semantic model, we show how a testing algorithm can distinguish, with a probability arbitrarily

Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation

Probabilistic Latent Semantic Analysis is a novel statistical technique for the analysis of two--mode and co-occurrence data, which has applications in information retrieval and filtering, natural language processing, machine learning from text, and in related areas. Compared to standard Latent

. In this paper we study the extension of classical testing theory to a probabilistic process algebra. We consider a generative interpretation of probabilities for a language with two choice operators (one internal and the other external), which are annotated with a probability p 2 (0; 1). We

We define a testing equivalence in the spirit of De Nicola and Hennessy for reactive probabilistic processes, i.e. for processes where the internal nondeterminism is due to random behaviour. We characterize the testing equivalence in terms of ready-traces. From the characterization it follows

Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a

ion Let E; E 0 be PCCS expressions. The inter-model abstraction rule IMARGR is defined by E ff[p] \Gamma\Gamma! i E 0 =) E ff[p= G (E;fffg)] ae \Gamma\Gamma\Gamma\Gamma\Gamma\Gamma! i E 0 This rule uses the generative normalization function to convert generative probabilities to reactive ones, thereby abstracting away from the relative probabilities between different actions. We can now define 'GR ('G (P )) as the reactive transition system that can be inferred from P 's generative transition system via IMARGR . By the same procedure as described at the end of Section 3.1, 'GR can be extended to a mapping 'GR : j GG ! j GR . Write P GR ¸ Q if P; Q 2 Pr are reactive bisimulation equivalent with respect to the transitions derivable from G+IMARGR , i.e. the theory obtained by adding IMARGR to the rules of Figure 7. The equivalence GR ¸ is defined just like R ¸ but using the cPDF ¯GR instead of ¯R . ¯GR is defined by ¯GR (P; ff; S) = X i2I R (=I G ) fj p i j G+ I...

Maximization algorithm for model fitting, which has shown excellent performance in practice. Probabilistic Latent Semantic Analysis has many applications, most prominently in information retrieval, natural language processing, machine learning from text, and in related areas. The paper presents perplexity

We introduce a symbolic model checking procedure for Probabilistic Computation Tree Logic PCTL over labelled Markov chains as models. Model checking for probabilistic logics typically involves solving linear equation systems in order to ascertain the probability of a given formula holding in a