Estimating machine learning performance 'in the wild' is both an important and unsolved problem. In this paper, we seek to examine, understand, and predict the pointwise competence of classification models. Our contributions are twofold: First, we establish a statistically rigorous definition of competence that generalizes the common notion of classifier confidence; second, we present the ALICE (Accurate Layerwise Interpretable Competence Estimation) Score, a pointwise competence estimator for any classifier. By considering distributional, data, and model uncertainty, ALICE empirically shows accurate competence estimation in common failure situations such as class-imbalanced datasets, out-of-distribution datasets, and poorly trained models. Our contributions allow us to accurately predict the competence of any classification model given any input and error function. We compare our score with state-of-the-art confidence estimators such as model confidence and Trust Score, and show significant improvements in competence prediction over these methods on datasets such as DIGITS, CIFAR10, and CIFAR100.

The importance of automated Facial Emotion Recognition (FER) grows the more common human-machine interactions become, which will only continue to increase dramatically with time. A common method to describe human sentiment or feeling is the categorical model the `7 basic emotions', consisting of `Angry', `Disgust', `Fear', `Happiness', `Sadness', `Surprise' and `Neutral'. The `Emotion Recognition in the Wild' (EmotiW) competition is now in its 7th year and has become the standard benchmark for measuring FER performance. The focus of this paper is the EmotiW sub-challenge of classifying videos in the `Acted Facial Expression in the Wild' (AFEW) dataset, consisting of both visual and audio modalities, into one of the above classes. Machine learning has exploded as a research topic in recent years, with advancements in `Deep Learning' a key part of this. Although Deep Learning techniques have been widely applied to the FER task by entrants in previous years, this paper has two main contributions: (i) to apply the latest `state-of-the-art' visual and temporal networks and (ii) exploring various methods of fusing features extracted from the visual and audio elements to enrich the information available to the final model making the prediction. There are a number of complex issues that arise when trying to classify emotions for `in-the-wild' video sequences, which the above two approaches attempt to directly address. There are some positive findings when comparing the results of this paper to past submissions, indicating that further research into the proposed methods and fine-tuning of the models deployed, could result in another step forwards in the field of automated FER.

Multimodal fusion frameworks for Human Action Recognition (HAR) using depth and inertial sensor data have been proposed over the years. In most of the existing works, fusion is performed at a single level (feature level or decision level), missing the opportunity to fuse rich mid-level features necessary for better classification. To address this shortcoming, in this paper, we propose three novel deep multilevel multimodal fusion frameworks to capitalize on different fusion strategies at various stages and to leverage the superiority of multilevel fusion. At input, we transform the depth data into depth images called sequential front view images (SFIs) and inertial sensor data into signal images. Each input modality, depth and inertial, is further made multimodal by taking convolution with the Prewitt filter. Creating "modality within modality" enables further complementary and discriminative feature extraction through Convolutional Neural Networks (CNNs). CNNs are trained on input images of each modality to learn low-level, high-level and complex features. Learned features are extracted and fused at different stages of the proposed frameworks to combine discriminative and complementary information. These highly informative features are served as input to a multi-class Support Vector Machine (SVM). We evaluate the proposed frameworks on three publicly available multimodal HAR datasets, namely, UTD Multimodal Human Action Dataset (MHAD), Berkeley MHAD, and UTD-MHAD Kinect V2. Experimental results show the supremacy of the proposed fusion frameworks over existing methods.

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian samples and/or outliers often makes it unreliable in practice. To this end, a robust formulation of PCA is derived based on the maximum correntropy criterion (MCC) so as to maximise the expected likelihood of Gaussian distributed reconstruction errors. In this way, the proposed solution reduces to a generalised power iteration, whereby: (i) robust estimates of the principal components are obtained even in the presence of outliers; (ii) the number of principal components need not be specified in advance; and (iii) the entire set of principal components can be obtained, unlike existing approaches. The advantages of the proposed maximum correntropy power iteration (MCPI) are demonstrated through an intuitive numerical example.

We propose in this paper a general framework for deriving loss functions for structured prediction. In our framework, the user chooses a convex set including the output space and provides an oracle for projecting onto that set. Given that oracle, our framework automatically generates a corresponding convex and smooth loss function. As we show, adding a projection as output layer provably makes the loss smaller. We identify the marginal polytope, the output space's convex hull, as the best convex set on which to project. However, because the projection onto the marginal polytope can sometimes be expensive to compute, we allow to use any convex superset instead, with potentially cheaper-to-compute projection. Since efficient projection algorithms are available for numerous convex sets, this allows us to construct loss functions for a variety of tasks. On the theoretical side, when combined with calibrated decoding, we prove that our loss functions can be used as a consistent surrogate for a (potentially non-convex) target loss function of interest. We demonstrate our losses on label ranking, ordinal regression and multilabel classification, confirming the improved accuracy enabled by projections.

The purpose of this paper is to introduced a new clustering methodology. This paper is divided into three parts. In the first part we have developed the axiomatic theory for the average silhouette width (ASW) index. There are different ways to investigate the quality and characteristics of clustering methods such as validation indices using simulations and real data experiments, model-based theory, and non-model-based theory known as the axiomatic theory. In this work we have not only taken the empirical approach of validation of clustering results through simulations, but also focus on the development of the axiomatic theory. In the second part we have presented a novel clustering methodology based on the optimization of the ASW index. We have considered the problem of estimation of number of clusters and finding clustering against this number simultaneously. Two algorithms are proposed. The proposed algorithms are evaluated against several partitioning and hierarchical clustering methods. An intensive empirical comparison of the different distance metrics on the various clustering methods is conducted. In the third part we have considered two application domains\textemdash novel single cell RNA sequencing datasets and rainfall data to cluster weather stations.

Financial fraud detection represents the challenge of finding anomalies in networks of financial transactions. In general, the anomaly detection (AD) is the problem of distinguishing between normal data samples with well defined patterns or signatures and those that do not conform to the expected profiles. The fraudulent behaviour in money laundering may manifest itself through unusual patterns in financial transaction networks. In such networks, nodes represents customers and the edges are transactions: a directed edge between two nodes illustrates that there is a money transfer in the respective direction, where the weight on the edge is the transferred amount. In this paper we present a survey on the fundamental anomaly detection techniques and then present briefly the relevant literature in connection with fraud detection context.

Combining insights from machine learning and quantum Monte Carlo, the stochastic reconfiguration method with neural network Ansatz states is a promising new direction for high precision ground state estimation of quantum many body problems. At present, the method is heuristic, lacking a proper theoretical foundation. We initiate a thorough analysis of the learning landscape, and show that it reveals universal behavior reflecting a combination of the underlying physics and of the learning dynamics. In particular, the spectrum of the quantum Fisher matrix of complex restricted Boltzmann machine states can dramatically change across a phase transition. In contrast to the spectral properties of the quantum Fisher matrix, the actual weights of the network at convergence do not reveal much information about the system or the dynamics. Furthermore, we identify a new measure of correlation in the state by analyzing entanglement the eigenvectors. We show that, generically, the learning landscape modes with least entanglement have largest eigenvalue, suggesting that correlations are encoded in large flat valleys of the learning landscape, favoring stable representations of the ground state.

Angular measurements are often modeled as circular random variables, where there are natural circular analogues of moments, including correlation. Because a product of circles is a torus, a d-dimensional vector of circular random variables lies on a d-dimensional torus. For such vectors we present here a class of graphical models, which we call torus graphs, based on the full exponential family with pairwise interactions. The topological distinction between a torus and Euclidean space has several important consequences. Our development was motivated by the problem of identifying phase coupling among oscillatory signals recorded from multiple electrodes in the brain: oscillatory phases across electrodes might tend to advance or recede together, indicating coordination across brain areas. The data analyzed here consisted of 24 phase angles measured repeatedly across 840 experimental trials (replications) during a memory task, where the electrodes were in 4 distinct brain regions, all known to be active while memories are being stored or retrieved. In realistic numerical simulations, we found that a standard pairwise assessment, known as phase locking value, is unable to describe multivariate phase interactions, but that torus graphs can accurately identify conditional associations. Torus graphs generalize several more restrictive approaches that have appeared in various scientific literatures, and produced intuitive results in the data we analyzed. Torus graphs thus unify multivariate analysis of circular data and present fertile territory for future research.

ERM and RERM are optimal estimators for regression problems when malicious outliers corrupt the labels CHINOT Geoffrey ENSAE, 5 avenue Henri Chatelier, 91120, Palaiseau, France email: geoffrey.chinot@ensae.fr Abstract: We study Empirical Risk Minimizers (ERM) and Regularized Empirical Risk Minimizers (RERM) for regression problems with convex and L-Lipschitz loss functions. We consider a setting where O malicious outliers may contaminate the labels. In that case, we show that the L 2-error rate is bounded by r N L O /N, where N is the total number of observations and r N is the L 2-error rate in the non-contaminated setting. When r N is minimax-rate-optimal in a non-contaminated setting, the rate r N L O /N is also minimax-rate-optimal when O outliers contaminate the label. The main results of the paper can be used for many non-regularized and regularized procedures under weak assumptions on the noise.