An axiomatized PDE model of deep neural networks

Inspired by the relation between deep neural network (DNN) and partial differential equations (PDEs), we study the general form of the PDE models of deep neural networks. To achieve this goal, we formulate DNN as an evolution operator from a simple base model. Based on several reasonable assumptions, we prove that the evolution operator is actually determined by convection-diffusion equation. This convection-diffusion equation model gives mathematical explanation for several effective networks. Moreover, we show that the convection-diffusion model improves the robustness and reduces the Rademacher complexity. Based on the convection-diffusion equation, we design a new training method for ResNets. Experiments validate the performance of the proposed method

Predicting continuous conflict perception with Bayesian Gaussian processes

Conflict is one of the most important phenomena of social life, but it is still largely neglected by the computing community. This work proposes an approach that detects common conversational social signals (loudness, overlapping speech, etc.) and predicts the conflict level perceived by human observers in continuous, non-categorical terms. The proposed regression approach is fully Bayesian and it adopts Automatic Relevance Determination to identify the social signals that influence most the outcome of the prediction. The experiments are performed over the SSPNet Conflict Corpus, a publicly available collection of 1430 clips extracted from televised political debates (roughly 12 hours of material for 138 subjects in total). The results show that it is possible to achieve a correlation close to 0.8 between actual and predicted conflict perception

Tree-Based Deep Mixture of Experts with Applications to Visual Saliency Prediction and Quality Robust Visual Recognition

abstract: Mixture of experts is a machine learning ensemble approach that consists of individual models that are trained to be ``experts'' on subsets of the data, and a gating network that provides weights to output a combination of the expert predictions. Mixture of experts models do not currently see wide use due to difficulty in training diverse experts and high computational requirements. This work presents modifications of the mixture of experts formulation that use domain knowledge to improve training, and incorporate parameter sharing among experts to reduce computational requirements. First, this work presents an application of mixture of experts models for quality robust visual recognition. First it is shown that human subjects outperform deep neural networks on classification of distorted images, and then propose a model, MixQualNet, that is more robust to distortions. The proposed model consists of ``experts'' that are trained on a particular type of image distortion. The final output of the model is a weighted sum of the expert models, where the weights are determined by a separate gating network. The proposed model also incorporates weight sharing to reduce the number of parameters, as well as increase performance. Second, an application of mixture of experts to predict visual saliency is presented. A computational saliency model attempts to predict where humans will look in an image. In the proposed model, each expert network is trained to predict saliency for a set of closely related images. The final saliency map is computed as a weighted mixture of the expert networks' outputs, with weights determined by a separate gating network. The proposed model achieves better performance than several other visual saliency models and a baseline non-mixture model. Finally, this work introduces a saliency model that is a weighted mixture of models trained for different levels of saliency. Levels of saliency include high saliency, which corresponds to regions where almost all subjects look, and low saliency, which corresponds to regions where some, but not all subjects look. The weighted mixture shows improved performance compared with baseline models because of the diversity of the individual model predictions.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Automatic Recognition and Generation of Affective Movements

Body movements are an important non-verbal communication medium through which affective states of the demonstrator can be discerned. For machines, the capability to recognize affective expressions of their users and generate appropriate actuated responses with recognizable affective content has the potential to improve their life-like attributes and to create an engaging, entertaining, and empathic human-machine interaction. This thesis develops approaches to systematically identify movement features most salient to affective expressions and to exploit these features to design computational models for automatic recognition and generation of affective movements. The proposed approaches enable 1) identifying which features of movement convey affective expressions, 2) the automatic recognition of affective expressions from movements, 3) understanding the impact of kinematic embodiment on the perception of affective movements, and 4) adapting pre-defined motion paths in order to "overlay" specific affective content. Statistical learning and stochastic modeling approaches are leveraged, extended, and adapted to derive a concise representation of the movements that isolates movement features salient to affective expressions and enables efficient and accurate affective movement recognition and generation. In particular, the thesis presents two new approaches to fixed-length affective movement representation based on 1) functional feature transformation, and 2) stochastic feature transformation (Fisher scores). The resulting representations are then exploited for recognition of affective expressions in movements and for salient movement feature identification. For functional representation, the thesis adapts dimensionality reduction techniques (namely, principal component analysis (PCA), Fisher discriminant analysis, Isomap) for functional datasets and applies the resulting reduction techniques to extract a minimal set of features along which affect-specific movements are best separable. Furthermore, the centroids of affect-specific clusters of movements in the resulting functional PCA subspace along with the inverse mapping of functional PCA are used to generate prototypical movements for each affective expression. The functional discriminative modeling is however limited to cases where affect-specific movements also have similar kinematic trajectories and does not address the interpersonal and stochastic variations inherent to bodily expression of affect. To account for these variations, the thesis presents a novel affective movement representation in terms of stochastically-transformed features referred to as Fisher scores. The Fisher scores are derived from affect-specific hidden Markov model encoding of the movements and exploited to discriminate between different affective expressions using a support vector machine (SVM) classification. Furthermore, the thesis presents a new approach for systematic identification of a minimal set of movement features most salient to discriminating between different affective expressions. The salient features are identified by mapping Fisher scores to a low-dimensional subspace where dependencies between the movements and their affective labels are maximized. This is done by maximizing Hilbert Schmidt independence criterion between the Fisher score representation of movements and their affective labels. The resulting subspace forms a suitable basis for affective movement recognition using nearest neighbour classification and retains the high recognition rates achieved by SVM classification in the Fisher score space. The dimensions of the subspace form a minimal set of salient features and are used to explore the movement kinematic and dynamic cues that connote affective expressions. Furthermore, the thesis proposes the use of movement notation systems from the dance community (specifically, the Laban system) for abstract coding and computational analysis of movement. A quantification approach for Laban Effort and Shape is proposed and used to develop a new computational model for affective movement generation. Using the Laban Effort and Shape components, the proposed generation approach searches a labeled dataset for movements that are kinematically similar to a desired motion path and convey a target emotion. A hidden Markov model of the identified movements is obtained and used with the desired motion path in the Viterbi state estimation. The estimated state sequence is then used to generate a novel movement that is a version of the desired motion path, modulated to convey the target emotion. Various affective human movement corpora are used to evaluate and demonstrate the efficacy of the developed approaches for the automatic recognition and generation of affective expressions in movements. Finally, the thesis assesses the human perception of affective movements and the impact of display embodiment and the observer's gender on the affective movement perception via user studies in which participants rate the expressivity of synthetically-generated and human-generated affective movements animated on anthropomorphic and non-anthropomorphic embodiments. The user studies show that the human perception of affective movements is mainly shaped by intended emotions, and that the display embodiment and the observer's gender can significantly impact the perception of affective movements

Investigating Social Interactions Using Multi-Modal Nonverbal Features

Every day, humans are involved in social situations and interplays, with the goal of sharing emotions and thoughts, establishing relationships with or acting on other human beings. These interactions are possible thanks to what is called social intelligence, which is the ability to express and recognize social signals produced during the interactions. These signals aid the information exchange and are expressed through verbal and non-verbal behavioral cues, such as facial expressions, gestures, body pose or prosody. Recently, many works have demonstrated that social signals can be captured and analyzed by automatic systems, giving birth to a relatively new research area called social signal processing, which aims at replicating human social intelligence with machines. In this thesis, we explore the use of behavioral cues and computational methods for modeling and understanding social interactions. Concretely, we focus on several behavioral cues in three specic contexts: rst, we analyze the relationship between gaze and leadership in small group interactions. Second, we expand our analysis to face and head gestures in the context of deception detection in dyadic interactions. Finally, we analyze the whole body for group detection in mingling scenarios

Robust subspace learning for static and dynamic affect and behaviour modelling

Machine analysis of human affect and behavior in naturalistic contexts has witnessed a growing attention in the last decade from various disciplines ranging from social and cognitive sciences to machine learning and computer vision. Endowing machines with the ability to seamlessly detect, analyze, model, predict as well as simulate and synthesize manifestations of internal emotional and behavioral states in real-world data is deemed essential for the deployment of next-generation, emotionally- and socially-competent human-centered interfaces. In this thesis, we are primarily motivated by the problem of modeling, recognizing and predicting spontaneous expressions of non-verbal human affect and behavior manifested through either low-level facial attributes in static images or high-level semantic events in image sequences. Both visual data and annotations of naturalistic affect and behavior naturally contain noisy measurements of unbounded magnitude at random locations, commonly referred to as ‘outliers’. We present here machine learning methods that are robust to such gross, sparse noise. First, we deal with static analysis of face images, viewing the latter as a superposition of mutually-incoherent, low-complexity components corresponding to facial attributes, such as facial identity, expressions and activation of atomic facial muscle actions. We develop a robust, discriminant dictionary learning framework to extract these components from grossly corrupted training data and combine it with sparse representation to recognize the associated attributes. We demonstrate that our framework can jointly address interrelated classification tasks such as face and facial expression recognition. Inspired by the well-documented importance of the temporal aspect in perceiving affect and behavior, we direct the bulk of our research efforts into continuous-time modeling of dimensional affect and social behavior. Having identified a gap in the literature which is the lack of data containing annotations of social attitudes in continuous time and scale, we first curate a new audio-visual database of multi-party conversations from political debates annotated frame-by-frame in terms of real-valued conflict intensity and use it to conduct the first study on continuous-time conflict intensity estimation. Our experimental findings corroborate previous evidence indicating the inability of existing classifiers in capturing the hidden temporal structures of affective and behavioral displays. We present here a novel dynamic behavior analysis framework which models temporal dynamics in an explicit way, based on the natural assumption that continuous- time annotations of smoothly-varying affect or behavior can be viewed as outputs of a low-complexity linear dynamical system when behavioral cues (features) act as system inputs. A novel robust structured rank minimization framework is proposed to estimate the system parameters in the presence of gross corruptions and partially missing data. Experiments on prediction of dimensional conflict and affect as well as multi-object tracking from detection validate the effectiveness of our predictive framework and demonstrate that for the first time that complex human behavior and affect can be learned and predicted based on small training sets of person(s)-specific observations.Open Acces