Bayesian nonparametric latent variable models

L’un des problèmes importants en apprentissage automatique est de déterminer la complexité du modèle à apprendre. Une trop grande complexité mène au surapprentissage, ce qui correspond à trouver des structures qui n’existent pas réellement dans les données, tandis qu’une trop faible complexité mène au sous-apprentissage, c’est-à-dire que l’expressivité du modèle est insuffisante pour capturer l’ensemble des structures présentes dans les données. Pour certains modèles probabilistes, la complexité du modèle se traduit par l’introduction d’une ou plusieurs variables cachées dont le rôle est d’expliquer le processus génératif des données. Il existe diverses approches permettant d’identifier le nombre approprié de variables cachées d’un modèle. Cette thèse s’intéresse aux méthodes Bayésiennes nonparamétriques permettant de déterminer le nombre de variables cachées à utiliser ainsi que leur dimensionnalité. La popularisation des statistiques Bayésiennes nonparamétriques au sein de la communauté de l’apprentissage automatique est assez récente. Leur principal attrait vient du fait qu’elles offrent des modèles hautement flexibles et dont la complexité s’ajuste proportionnellement à la quantité de données disponibles. Au cours des dernières années, la recherche sur les méthodes d’apprentissage Bayésiennes nonparamétriques a porté sur trois aspects principaux : la construction de nouveaux modèles, le développement d’algorithmes d’inférence et les applications. Cette thèse présente nos contributions à ces trois sujets de recherches dans le contexte d’apprentissage de modèles à variables cachées. Dans un premier temps, nous introduisons le Pitman-Yor process mixture of Gaussians, un modèle permettant l’apprentissage de mélanges infinis de Gaussiennes. Nous présentons aussi un algorithme d’inférence permettant de découvrir les composantes cachées du modèle que nous évaluons sur deux applications concrètes de robotique. Nos résultats démontrent que l’approche proposée surpasse en performance et en flexibilité les approches classiques d’apprentissage. Dans un deuxième temps, nous proposons l’extended cascading Indian buffet process, un modèle servant de distribution de probabilité a priori sur l’espace des graphes dirigés acycliques. Dans le contexte de réseaux Bayésien, ce prior permet d’identifier à la fois la présence de variables cachées et la structure du réseau parmi celles-ci. Un algorithme d’inférence Monte Carlo par chaîne de Markov est utilisé pour l’évaluation sur des problèmes d’identification de structures et d’estimation de densités. Dans un dernier temps, nous proposons le Indian chefs process, un modèle plus général que l’extended cascading Indian buffet process servant à l’apprentissage de graphes et d’ordres. L’avantage du nouveau modèle est qu’il admet les connections entres les variables observables et qu’il prend en compte l’ordre des variables. Nous présentons un algorithme d’inférence Monte Carlo par chaîne de Markov avec saut réversible permettant l’apprentissage conjoint de graphes et d’ordres. L’évaluation est faite sur des problèmes d’estimations de densité et de test d’indépendance. Ce modèle est le premier modèle Bayésien nonparamétrique permettant d’apprendre des réseaux Bayésiens disposant d’une structure complètement arbitraire.

Mining trading partners’ preferences for efficient multi-issue bargaining in E‑business

Classical negotiation models are weak in supporting real-world business negotiations because these models often assume that the preference information of each negotiator is made public. Although parametric learning methods have been proposed for acquiring the preference information of negotiation opponents, these methods suffer from the strong assumptions about the specific utility function and negotiation mechanism employed by the opponents. Consequently, it is difficult to apply these learning methods to the heterogeneous negotiation agents participating in e‑marketplaces. This paper illustrates the design, development, and evaluation of a nonparametric negotiation knowledge discovery method which is underpinned by the well-known Bayesian learning paradigm. According to our empirical testing, the novel knowledge discovery method can speed up the negotiation processes while maintaining negotiation effectiveness. To the best of our knowledge, this is the first nonparametric negotiation knowledge discovery method developed and evaluated in the context of multi-issue bargaining over e‑marketplaces.

Knowledge discovery for adaptive negotiation agents in e-marketplaces

Intelligent software agents are promising in improving the effectiveness of e-marketplaces for e-commerce. Although a large amount of research has been conducted to develop negotiation protocols and mechanisms for e-marketplaces, existing negotiation mechanisms are weak in dealing with complex and dynamic negotiation spaces often found in e-commerce. This paper illustrates a novel knowledge discovery method and a probabilistic negotiation decision making mechanism to improve the performance of negotiation agents. Our preliminary experiments show that the probabilistic negotiation agents empowered by knowledge discovery mechanisms are more effective and efficient than the Pareto optimal negotiation agents in simulated e-marketplaces.

Neural and computational representations of decision variables

These studies explore how, where, and when representations of variables critical to decision-making are represented in the brain. In order to produce a decision, humans must first determine the relevant stimuli, actions, and possible outcomes before applying an algorithm that will select an action from those available. When choosing amongst alternative stimuli, the framework of value-based decision-making proposes that values are assigned to the stimuli and that these values are then compared in an abstract “value space” in order to produce a decision. Despite much progress, in particular regarding the pinpointing of ventromedial prefrontal cortex (vmPFC) as a region that encodes the value, many basic questions remain. In Chapter 2, I show that distributed BOLD signaling in vmPFC represents the value of stimuli under consideration in a manner that is independent of the type of stimulus it is. Thus the open question of whether value is represented in abstraction, a key tenet of value-based decision-making, is confirmed. However, I also show that stimulus-dependent value representations are also present in the brain during decision-making and suggest a potential neural pathway for stimulus-to-value transformations that integrates these two results.

More broadly speaking, there is both neural and behavioral evidence that two distinct control systems are at work during action selection. These two systems compose the “goal-directed system”, which selects actions based on an internal model of the environment, and the “habitual” system, which generates responses based on antecedent stimuli only. Computational characterizations of these two systems imply that they have different informational requirements in terms of input stimuli, actions, and possible outcomes. Associative learning theory predicts that the habitual system should utilize stimulus and action information only, while goal-directed behavior requires that outcomes as well as stimuli and actions be processed. In Chapter 3, I test whether areas of the brain hypothesized to be involved in habitual versus goal-directed control represent the corresponding theorized variables.

The question of whether one or both of these neural systems drives Pavlovian conditioning is less well-studied. Chapter 4 describes an experiment in which subjects were scanned while engaged in a Pavlovian task with a simple non-trivial structure. After comparing a variety of model-based and model-free learning algorithms (thought to underpin goal-directed and habitual decision-making, respectively), it was found that subjects’ reaction times were better explained by a model-based system. In addition, neural signaling of precision, a variable based on a representation of a world model, was found in the amygdala. These data indicate that the influence of model-based representations of the environment can extend even to the most basic learning processes.

Knowledge of the state of hidden variables in an environment is required for optimal inference regarding the abstract decision structure of a given environment and therefore can be crucial to decision-making in a wide range of situations. Inferring the state of an abstract variable requires the generation and manipulation of an internal representation of beliefs over the values of the hidden variable. In Chapter 5, I describe behavioral and neural results regarding the learning strategies employed by human subjects in a hierarchical state-estimation task. In particular, a comprehensive model fit and comparison process pointed to the use of "belief thresholding". This implies that subjects tended to eliminate low-probability hypotheses regarding the state of the environment from their internal model and ceased to update the corresponding variables. Thus, in concert with incremental Bayesian learning, humans explicitly manipulate their internal model of the generative process during hierarchical inference consistent with a serial hypothesis testing strategy.

Reconstruction of arbitrary biochemical reaction networks: A compressive sensing approach

Reconstruction of biochemical reaction networks (BRN) and genetic regulatory networks (GRN) in particular is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and rational functions are typically used to model biochemical reaction networks. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data quite difficult. In this paper, we present a network reconstruction algorithm that can deal with ODE model descriptions containing polynomial and rational functions. Rather than identifying the parameters of linear or nonlinear ODEs characterised by pre-defined equation structures, our methodology allows us to determine the nonlinear ODEs structure together with their associated parameters. To solve the network reconstruction problem, we cast it as a compressive sensing (CS) problem and use sparse Bayesian learning (SBL) algorithms as a computationally efficient and robust way to obtain its solution. © 2012 IEEE.

Efficient Marginal Likelihood Computation for Gaussian Process Regression

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional hyperparameters which need to be tuned in order to achieve optimum predictive performance; this operation can be efficiently performed in an Empirical Bayes fashion by maximizing the posterior marginal likelihood of the observed data. Since the score function of this optimization problem is in general characterized by the presence of local optima, it is necessary to resort to global optimization strategies, which require a large number of function evaluations. Given that the evaluation is usually computationally intensive and badly scaled with respect to the dataset size, the maximum number of observations that can be treated simultaneously is quite limited. In this paper, we consider the case of hyperparameter tuning in Gaussian process regression. A straightforward implementation of the posterior log-likelihood for this model requires O(N^3) operations for every iteration of the optimization procedure, where N is the number of examples in the input dataset. We derive a novel set of identities that allow, after an initial overhead of O(N^3), the evaluation of the score function, as well as the Jacobian and Hessian matrices, in O(N) operations. We prove how the proposed identities, that follow from the eigendecomposition of the kernel matrix, yield a reduction of several orders of magnitude in the computation time for the hyperparameter optimization problem. Notably, the proposed solution provides computational advantages even with respect to state of the art approximations that rely on sparse kernel matrices.

INFO6003 (2013) Towards a formal framework for computation trust -- paper

the introduction of this research paper (especially pg 2-4) and its list of references may be useful to clarify the notions of Bayesian learning applied to trust as explained in the lectures. This is optional reading

Probability distributions or point predictions? Survey forecasts of US output growth and inflation

We consider whether survey respondents’ probability distributions, reported as histograms, provide reliable and coherent point predictions, when viewed through the lens of a Bayesian learning model. We argue that a role remains for eliciting directly-reported point predictions in surveys of professional forecasters.

Predicting amount of saleable products using neural network metamodels of casthouses

This study aims at developing abstract metamodels for approximating highly nonlinear relationships within a metal casting plant. Metal casting product quality nonlinearly depends on many controllable and uncontrollable factors. For improving the productivity of the system, it is vital for operation planners to predict in advance the amount of high quality products. Neural networks metamodels are developed and applied in this study for predicting the amount of saleable products. Training of metamodels is done using the Levenberg-Marquardt and Bayesian learning methods. Statistical measures are calculated for the developed metamodels over a grid of neural network structures. Demonstrated results indicate that Bayesian-based neural network metamodels outperform the Levenberg-Marquardt-based metamodels in terms of both prediction accuracy and robustness to the metamodel complexity. In contrast, the latter metamodels are computationally less expensive and generate the results more quickly.

Parameter estimation of the BOLD fMRI model within a general particle filter framework

This work demonstrates a novel Bayesian learning approach for model based analysis of Functional Magnetic Resonance (fMRI) data. We use a physiologically inspired hemodynamic model and investigate a method to simultaneously infer the neural activity together with hidden state and the physiological parameter of the model. This joint estimation problem is still an open topic. In our work we use a Particle Filter accompanied with a kernel smoothing approach to address this problem within a general filtering framework. Simulation results show that the proposed method is a consistent approach and has a good potential to be enhanced for further fMRI data analysis.

Probabilistic models for the prediction of a ship performance in dynamic ice

We introduce two probabilistic, data-driven models that predict a ship's speed and the situations where a ship is probable to get stuck in ice based on the joint effect of ice features such as the thickness and concentration of level ice, ice ridges, rafted ice, moreover ice compression is considered. To develop the models to datasets were utilized. First, the data from the Automatic Identification System about the performance of a selected ship was used. Second, a numerical ice model HELMI, developed in the Finnish Meteorological Institute, provided information about the ice field. The relations between the ice conditions and ship movements were established using Bayesian learning algorithms. The case study presented in this paper considers a single and unassisted trip of an ice-strengthened bulk carrier between two Finnish ports in the presence of challenging ice conditions, which varied in time and space. The obtained results show good prediction power of the models. This means, on average 80% for predicting the ship's speed within specified bins, and above 90% for predicting cases where a ship may get stuck in ice. We expect this new approach to facilitate the safe and effective route selection problem for ice-covered waters where the ship performance is reflected in the objective function.

Gaussian processes:iterative sparse approximations

In recent years there has been an increased interest in applying non-parametric methods to real-world problems. Significant research has been devoted to Gaussian processes (GPs) due to their increased flexibility when compared with parametric models. These methods use Bayesian learning, which generally leads to analytically intractable posteriors. This thesis proposes a two-step solution to construct a probabilistic approximation to the posterior. In the first step we adapt the Bayesian online learning to GPs: the final approximation to the posterior is the result of propagating the first and second moments of intermediate posteriors obtained by combining a new example with the previous approximation. The propagation of em functional forms is solved by showing the existence of a parametrisation to posterior moments that uses combinations of the kernel function at the training points, transforming the Bayesian online learning of functions into a parametric formulation. The drawback is the prohibitive quadratic scaling of the number of parameters with the size of the data, making the method inapplicable to large datasets. The second step solves the problem of the exploding parameter size and makes GPs applicable to arbitrarily large datasets. The approximation is based on a measure of distance between two GPs, the KL-divergence between GPs. This second approximation is with a constrained GP in which only a small subset of the whole training dataset is used to represent the GP. This subset is called the em Basis Vector, or BV set and the resulting GP is a sparse approximation to the true posterior. As this sparsity is based on the KL-minimisation, it is probabilistic and independent of the way the posterior approximation from the first step is obtained. We combine the sparse approximation with an extension to the Bayesian online algorithm that allows multiple iterations for each input and thus approximating a batch solution. The resulting sparse learning algorithm is a generic one: for different problems we only change the likelihood. The algorithm is applied to a variety of problems and we examine its performance both on more classical regression and classification tasks and to the data-assimilation and a simple density estimation problems.

On the Quality of Decision Functions in Pattern Recognition

The problem of decision functions quality in pattern recognition is considered. An overview of the approaches to the solution of this problem is given. Within the Bayesian framework, we suggest an approach based on the Bayesian interval estimates of quality on a finite set of events.

Three essays on entrepreneurial motivation, entry, exit and monetary rewards

This dissertation analyzes rewards and motivations of self-employment. In light of recent research contributions of Barton Hamilton (2000), which find entrepreneurship not as financially rewarding as wage work, my dissertation attempts to both verify and explain this claim. The first essay proposes a theoretical model of evolution of erroneous earnings expectations on part of a nascent entrepreneur. Inability to observe, survey, and take into account all of the returns to entrepreneurship prior to business entry creates a biased set of beliefs on part of the potential entrants. Using Bayesian learning, a nascent entrepreneur starting out with correct perception of profit distribution arrives at erroneous beliefs by incorporating limited information collected from existing businesses. An observed distribution of surviving businesses would exhibit higher earnings because of previous, unobserved, business failure entrepreneur get an overly positive view of her profit potential. Hence, the chapter offers a unique method of modeling overconfidence. The second essay undertakes dynamic empirical comparison of earnings received by business owners and their wage counterparts. Using Survey of Income and Program Participation (SIPP) I examine both short and long run returns to entrepreneurship comparing theses rewards to wage earners returns. I pay particular attention to transitions into and out of business ownership. I estimate entire earnings distribution. To characterize dynamic aspect of changes to individuals’ earnings I split the income distribution into five income quintiles and follow survey participants over the period of seven years. I find that period-to-period transitions to be Markovian. I find business tenure to be short, business ownership is costly in the short and rewarding in the long run. The third essay considered different reporting schemes applied to the self-employed. It is another empirical investigation of entrepreneurial earning uses Panel Study of Income Dynamics (PSID). I find entrepreneurs while reporting lower than wage workers earnings enjoy significant consumption premiums. I observe evidence of income underreporting by entrepreneurs. This finding suggests a need for better earning comparison metrics and proposes to use consumption rather than income metrics for future comparisons.

Three Essays on a Longitudinal Analysis of Business Start-ups using the Kauffman Firm Survey

This dissertation focused on the longitudinal analysis of business start-ups using three waves of data from the Kauffman Firm Survey. The first essay used the data from years 2004-2008, and examined the simultaneous relationship between a firm’s capital structure, human resource policies, and its impact on the level of innovation. The firm leverage was calculated as, debt divided by total financial resources. Index of employee well-being was determined by a set of nine dichotomous questions asked in the survey. A negative binomial fixed effects model was used to analyze the effect of employee well-being and leverage on the count data of patents and copyrights, which were used as a proxy for innovation. The paper demonstrated that employee well-being positively affects the firm's innovation, while a higher leverage ratio had a negative impact on the innovation. No significant relation was found between leverage and employee well-being. The second essay used the data from years 2004-2009, and inquired whether a higher entrepreneurial speed of learning is desirable, and whether there is a linkage between the speed of learning and growth rate of the firm. The change in the speed of learning was measured using a pooled OLS estimator in repeated cross-sections. There was evidence of a declining speed of learning over time, and it was concluded that a higher speed of learning is not necessarily a good thing, because speed of learning is contingent on the entrepreneur's initial knowledge, and the precision of the signals he receives from the market. Also, there was no reason to expect speed of learning to be related to the growth of the firm in one direction over another. The third essay used the data from years 2004-2010, and determined the timing of diversification activities by the business start-ups. It captured when a start-up diversified for the first time, and explored the association between an early diversification strategy adopted by a firm, and its survival rate. A semi-parametric Cox proportional hazard model was used to examine the survival pattern. The results demonstrated that firms diversifying at an early stage in their lives show a higher survival rate; however, this effect fades over time.