Learning Topic Models and Latent Bayesian Networks Under Expansion Constraints

Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including probabilistic topic models and latent linear Bayesian networks, using only second-order observed moments. The sufficient conditions for identifiability of these models are primarily based on weak expansion constraints on the topic-word matrix, for topic models, and on the directed acyclic graph, for Bayesian networks. Because no assumptions are made on the distribution among the latent variables, the approach can handle arbitrary correlations among the topics or latent factors. In addition, a tractable learning method via $\ell_1$ optimization is proposed and studied in numerical experiments.Comment: 38 pages, 6 figures, 2 tables, applications in topic models and Bayesian networks are studied. Simulation section is adde

Open TURNS: An industrial software for uncertainty quantification in simulation

The needs to assess robust performances for complex systems and to answer tighter regulatory processes (security, safety, environmental control, and health impacts, etc.) have led to the emergence of a new industrial simulation challenge: to take uncertainties into account when dealing with complex numerical simulation frameworks. Therefore, a generic methodology has emerged from the joint effort of several industrial companies and academic institutions. EDF R&D, Airbus Group and Phimeca Engineering started a collaboration at the beginning of 2005, joined by IMACS in 2014, for the development of an Open Source software platform dedicated to uncertainty propagation by probabilistic methods, named OpenTURNS for Open source Treatment of Uncertainty, Risk 'N Statistics. OpenTURNS addresses the specific industrial challenges attached to uncertainties, which are transparency, genericity, modularity and multi-accessibility. This paper focuses on OpenTURNS and presents its main features: openTURNS is an open source software under the LGPL license, that presents itself as a C++ library and a Python TUI, and which works under Linux and Windows environment. All the methodological tools are described in the different sections of this paper: uncertainty quantification, uncertainty propagation, sensitivity analysis and metamodeling. A section also explains the generic wrappers way to link openTURNS to any external code. The paper illustrates as much as possible the methodological tools on an educational example that simulates the height of a river and compares it to the height of a dyke that protects industrial facilities. At last, it gives an overview of the main developments planned for the next few years

A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification

This paper studies generic properties of Markov perfect equilibria in dynamic stochastic games. We show that almost all dynamic stochastic games have a finite number of locally isolated Markov perfect equilibria. These equilibria are essential and strongly stable. Moreover, they all admit purification. To establish these results, we introduce a notion of regularity for dynamic stochastic games and exploit a simple connection between normal form and dynamic stochastic games.Dynamic stochastic games, Markov perfect equilibrium, regularity, genericity, finiteness, strong stability, essentiality, purifiability, estimation, computation, repeated games

Examples of L^2-Complete and Boundedly-Complete Distributions

Completeness and bounded-completeness conditions are used increasingly in econometrics to obtain nonparametric identification in a variety of models from nonparametric instrumental variable regression to non-classical measurement error models. However, distributions that are known to be complete or boundedly complete are somewhat scarce. In this paper, we consider an L^2-completeness condition that lies between completeness and bounded completeness. We construct broad (nonparametric) classes of distributions that are L^2-complete and boundedly complete. The distributions can have any marginal distributions and a wide range of strengths of dependence. Examples of L^2-incomplete distributions also are provided.Bivariate distribution, Bounded completeness, Canonical correlation, Completeness, Identification, Measurement error, Nonparametric instrumental variable regression

Shape and Illumination from Shading Using the Generic Viewpoint Assumption

The Generic Viewpoint Assumption (GVA) states that the position of the viewer or the light in a scene is not special. Thus, any estimated parameters from an observation should be stable under small perturbations such as object, viewpoint or light positions. The GVA has been analyzed and quantified in previous works, but has not been put to practical use in actual vision tasks. In this paper, we show how to utilize the GVA to estimate shape and illumination from a single shading image, without the use of other priors. We propose a novel linearized Spherical Harmonics (SH) shading model which enables us to obtain a computationally efficient form of the GVA term. Together with a data term, we build a model whose unknowns are shape and SH illumination. The model parameters are estimated using the Alternating Direction Method of Multipliers embedded in a multi-scale estimation framework. In this prior-free framework, we obtain competitive shape and illumination estimation results under a variety of models and lighting conditions, requiring fewer assumptions than competing methods.National Science Foundation (U.S.). Directorate for Computer and Information Science and Engineering/Division of Information & Intelligent Systems (Award 1212928)Qatar Computing Research Institut

Awareness as an Equilibrium Notion: Normal-Form Games

We study normal-form games where parts of the games may not be common knowledge. Agents may be aware only of some facts describing the game. An awareness architecture is given by agents' awareness, and an infinite regress of conjectures about other agents and their conjectures. The problem is specified by the true underlying normal-form game, and by the set of possible awareness architectures. Awareness equilibrium is given by a feasible awareness architecture for each agent, strategies that are played and these strategies have to be consistent with the awareness architectures and agents' rationality. We first study games with complete information, where each player may be aware of a subset of the set of possible actions. We then study games with incomplete information, where each player may be aware of a subset of the set of types and probability over types. Our results illustrate how a departure from the assumption of common knowledge alters equilibium predictions