Bayesian networks and information theory for audio-visual perception modeling

Thanks to their different senses, human observers acquire multiple information coming from their environment. Complex cross-modal interactions occur during this perceptual process. This article proposes a framework to analyze and model these interactions through a rigorous and systematic data-driven process. This requires considering the general relationships between the physical events or factors involved in the process, not only in quantitative terms, but also in term of the influence of one factor on another. We use tools from information theory and probabilistic reasoning to derive relationships between the random variables of interest, where the central notion is that of conditional independence. Using mutual information analysis to guide the model elicitation process, a probabilistic causal model encoded as a Bayesian network is obtained. We exemplify the method by using data collected in an audio-visual localization task for human subjects, and we show that it yields a well-motivated model with good predictive ability. The model elicitation process offers new prospects for the investigation of the cognitive mechanisms of multisensory perception.

Error handling in multimodal voice-enabled interfaces of tour-guide robots using graphical models

Plamen Prodanov

Mobile service robots are going to play an increasing role in the society of humans. Voice-enabled interaction with service robots becomes very important, if such robots are to be deployed in real-world environments and accepted by the vast majority of potential human users. The research presented in this thesis addresses the problem of speech recognition integration in an interactive voice-enabled interface of a service robot, in particular a tour-guide robot. The task of a tour-guide robot is to engage visitors to mass exhibitions (users) in dialogue providing the services it is designed for (e.g. exhibit presentations) within a limited time. In managing tour-guide dialogues, extracting the user goal (intention) for requesting a particular service at each dialogue state is the key issue. In mass exhibition conditions speech recognition errors are inevitable because of noisy speech and uncooperative users of robots with no prior experience in robotics. They can jeopardize the user goal identification. Wrongly identified user goals can lead to communication failures. Therefore, to reduce the risk of such failures, methods for detecting and compensating for communication failures in human-robot dialogue are needed. During the short-term interaction with visitors, the interpretation of the user goal at each dialogue state can be improved by combining speech recognition in the speech modality with information from other available robot modalities. The methods presented in this thesis exploit probabilistic models for fusing information from speech and auxiliary modalities of the robot for user goal identification and communication failure detection. To compensate for the detected communication failures we investigate multimodal methods for recovery from communication failures. To model the process of modality fusion, taking into account the uncertainties in the information extracted from each input modality during human-robot interaction, we use the probabilistic framework of Bayesian networks. Bayesian networks are graphical models that represent a joint probability function over a set of random variables. They are used to model the dependencies among variables associated with the user goals, modality related events (e.g. the event of user presence that is inferred from the laser scanner modality of the robot), and observed modality features providing evidence in favor of these modality events. Bayesian networks are used to calculate posterior probabilities over the possible user goals at each dialogue state. These probabilities serve as a base in deciding if the user goal is valid, i.e. if it can be mapped into a tour-guide service (e.g. exhibit presentation) or is undefined – signaling a possible communication failure. The Bayesian network can be also used to elicit probabilities over the modality events revealing information about the possible cause for a communication failure. Introducing new user goal aspects (e.g. new modality events and related features) that provide auxiliary information for detecting communication failures makes the design process cumbersome, calling for a systematic approach in the Bayesian network modelling. Generally, introducing new variables for user goal identification in the Bayesian networks can lead to complex and computationally expensive models. In order to make the design process more systematic and modular, we adapt principles from the theory of grounding in human communication. When people communicate, they resolve understanding problems in a collaborative joint effort of providing evidence of common shared knowledge (grounding). We use Bayesian network topologies, tailored to limited computational resources, to model a state-based grounding model fusing information from three different input modalities (laser, video and speech) to infer possible grounding states. These grounding states are associated with modality events showing if the user is present in range for communication, if the user is attending to the interaction, whether the speech modality is reliable, and if the user goal is valid. The state-based grounding model is used to compute probabilities that intermediary grounding states have been reached. This serves as a base for detecting if the the user has reached the final grounding state, or wether a repair dialogue sequence is needed. In the case of a repair dialogue sequence, the tour-guide robot can exploit the multiple available modalities along with speech. For example, if the user has failed to reach the grounding state related to her/his presence in range for communication, the robot can use its move modality to search and attract the attention of the visitors. In the case when speech recognition is detected to be unreliable, the robot can offer the alternative use of the buttons modality in the repair sequence. Given the probability of each grounding state, and the dialogue sequence that can be executed in the next dialogue state, a tour-guide robot has different preferences on the possible dialogue continuation. If the possible dialogue sequences at each dialogue state are defined as actions, the introduced principle of maximum expected utility (MEU) provides an explicit way of action selection, based on the action utility, given the evidence about the user goal at each dialogue state. Decision networks, constructed as graphical models based on Bayesian networks are proposed to perform MEU-based decisions, incorporating the utility of the actions to be chosen at each dialogue state by the tour-guide robot. These action utilities are defined taking into account the tour-guide task requirements. The proposed graphical models for user goal identification and dialogue error handling in human-robot dialogue are evaluated in experiments with multimodal data. These data were collected during the operation of the tour-guide robot RoboX at the Autonomous System Lab of EPFL and at the Swiss National Exhibition in 2002 (Expo.02). The evaluation experiments use component and system level metrics for technical (objective) and user-based (subjective) evaluation. On the component level, the technical evaluation is done by calculating accuracies, as objective measures of the performance of the grounding model, and the resulting performance of the user goal identification in dialogue. The benefit of the proposed error handling framework is demonstrated comparing the accuracy of a baseline interactive system, employing only speech recognition for user goal identification, and a system equipped with multimodal grounding models for error handling.

EPFL2006

High-Dimensional Inference on Dense Graphs with Applications to Coding Theory and Machine Learning

Mohamad Baker Dia

We are living in the era of "Big Data", an era characterized by a voluminous amount of available data. Such amount is mainly due to the continuing advances in the computational capabilities for capturing, storing, transmitting and processing data. However, it is not always the volume of data that matters, but rather the "relevant" information that resides in it. Exactly 70 years ago, Claude Shannon, the father of information theory, was able to quantify the amount of information in a communication scenario based on a probabilistic model of the data. It turns out that Shannon's theory can be adapted to various probability-based information processing fields, ranging from coding theory to machine learning. The computation of some information theoretic quantities, such as the mutual information, can help in setting fundamental limits and devising more efficient algorithms for many inference problems. This thesis deals with two different, yet intimately related, inference problems in the fields of coding theory and machine learning. We use Bayesian probabilistic formulations for both problems, and we analyse them in the asymptotic high-dimensional regime. The goal of our analysis is to assess the algorithmic performance on the first hand and to predict the Bayes-optimal performance on the second hand, using an information theoretic approach. To this end, we employ powerful analytical tools from statistical physics. The first problem is a recent forward-error-correction code called sparse superposition code. We consider the extension of such code to a large class of noisy channels by exploiting the similarity with the compressed sensing paradigm. Moreover, we show the amenability of sparse superposition codes to perform joint distribution matching and channel coding. In the second problem, we study symmetric rank-one matrix factorization, a prominent model in machine learning and statistics with many applications ranging from community detection to sparse principal component analysis. We provide an explicit expression for the normalized mutual information and the minimum mean-square error of this model in the asymptotic limit. This allows us to prove the optimality of a certain iterative algorithm on a large set of parameters. A common feature of the two problems stems from the fact that both of them are represented on dense graphical models. Hence, similar message-passing algorithms and analysis tools can be adopted. Furthermore, spatial coupling, a new technique introduced in the context of low-density parity-check (LDPC) codes, can be applied to both problems. Spatial coupling is used in this thesis as a "construction technique" to boost the algorithmic performance and as a "proof technique" to compute some information theoretic quantities. Moreover, both of our problems retain close connections with spin glass models studied in statistical mechanics of disordered systems. This allows us to use sophisticated techniques developed in statistical physics. In this thesis, we use the potential function predicted by the replica method in order to prove the threshold saturation phenomenon associated with spatially coupled models. Moreover, one of the main contributions of this thesis is proving that the predictions given by the "heuristic" replica method are exact. Hence, our results could be of great interest for the statistical physics community as well, as they help to set a rigorous mathematical foundation of the replica predictions.

EPFL2018

Statistical Physics Methods for Community Detection

Chun Lam Chan

This thesis is devoted to information-theoretic aspects of community detection. The importance of community detection is due to the massive amount of scientific data today that describes relationships between items from a network, e.g., a social network. Items from this network can be inherently partitioned into a known number of communities, but the partition can only be inferred from the data. To estimate the underlying partition, data scientists can apply any type of advanced statistical techniques; but the data could be very noisy, or the number of data is inadequate. A fundamental question here is about the possibility of weak recovery: does the data contain a sufficient amount of information that enables us to produce a non-trivial estimate of the partition? For the purpose of mathematical analysis, the above problem can be formulated as Bayesian inference on generative models. These models, including the stochastic block model (SBM) and censored block model (CBM), consider a random graph generated based on a hidden partition that divides the nodes in the graph into labelled groups. In the SBM, nodes are connected with a probability depending on the labels of the endpoints. Whereas, in the CBM, hidden variables are measured through a noisy channel, and the measurement outcomes form a weighted graph. In both models, inference is the task of recovering the hidden partition from the observed graph. The criteria for weak recovery can be studied via an information-theoretic quantity called mutual information. Once the asymptotic mutual information is computed, phase transitions for the weak recovery can be located. This thesis pertains to rigorous derivations of single-letter variational expressions for the asymptotic mutual information for models in community detection. These variational expressions, known as the replica predictions, come from heuristic methods of statistical physics. We present our development of new rigorous methods for confirming the replica predictions. These methods are based on extending the recently introduced adaptive interpolation method. We prove the replica prediction for the SBM in the dense-graph regime with two groups of asymmetric size. The existing proofs in the literature are indirect, as they involve mapping the model to an external problem whose mutual information is determined by a combination of methods. Here, on the contrary, we provide a self-contained and direct proof. Next, we extend this method to sparse models. Before this thesis, adaptive interpolation was known for providing a conceptually simple proof for replica predictions for dense graphs. Whereas, for a sparse graph, the replica prediction involves a more complicated variational expression, and rigorous confirmations are often lacking or obtained by rather complicated methods. Therefore, we focus on a simple version of CBM on sparse graphs, where hidden variables are measured through a binary erasure channel, for which we fully prove the replica prediction by the adaptive interpolation. The key for extending the adaptive interpolation to a broader class of sparse models is a concentration result for the so-called "multi-overlaps". This concentration forms the basis of the replica "symmetric" prediction. We prove this concentration result for a related sparse model in the context of physics. This provides inspiration for further development of the adaptive interpolation.

EPFL2019