We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model. 1.

and industry are relying more and more on science’s advanced methods to determine reliability. Unfortunately, political, economic, time, and other constraints imposed by the real world inhibit the ability of researchers to calculate reliability efficiently and accurately. Because of such constraints, reliability must undergo an evolutionary change. The first step in this evolution is to reinterpret the concept so that it meets the new century’s needs. The next step is to quantify reliability using both empirical methods and auxiliary data sources, such as expert knowledge, corporate memory, and mathematical modeling and simulation. 1

In some situations, a decision is best represented by an incompletely analyzed act: conditionally to a certain event, the consequences of the decision on sub-events are perfectly known and uncertainty becomes expressable through probabilities, whereas the plausibility of this event itself remains vague and the decision outcome on the complementary event is imprecisely known. In this framework, we study an axiomatic decision model and prove a representation theorem. Decision criteria must aggregate partial evaluations consisting in: i) the conditional expected utility associated with the analyzed part of the decision and ii) the best and worst outcomes of its non-analyzed part.

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The theory of probability, based on very general rules referred to as the Cox-Pólya-Jaynes Desiderata, can be used both as a theory of random mass phenomena and as a quantitative theory of plausible inference about the parameters of sampling distributions. The existing applications of the Desiderata must be extended in order to allow for consistent inferences in the limit of complete a priori ignorance about the values of the parameters. Since the limits of consistent quantitative inference from incomplete information can clearly be established, the developed theory is necessarily an effective one. It is interesting to note that when applying the Desiderata strictly, we find no contradictions between the so-called Bayesian and frequentist schools of inductive reasoning.