Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced cluster sizes since they tend to emphasize cut sizes over cut values. We propose a graph partitioning problem that seeks minimum cut partitions under minimum size constraints on partitions to deal with imbalanced cluster sizes. Our approach parameterizes a family of graphs by adaptively modulating node degrees on a fixed node set, yielding a set of parameter dependent cuts reflecting varying levels of imbalance. The solution to our problem is then obtained by optimizing over these parameters. We present rigorous limit cut analysis results to justify our approach and demonstrate the superiority of our method through experiments on synthetic and real datasets for data clustering, semi-supervised learning and community detection.

We consider the setting where a collection of time series, modeled as random processes, evolve in a causal manner, and one is interested in learning the graph governing the relationships of these processes. A special case of wide interest and applicability is the setting where the noise is Gaussian and relationships are Markov and linear. We study this setting with two additional features: firstly, each random process has a hidden (latent) state, which we use to model the internal memory possessed by the variables (similar to hidden Markov models). Secondly, each variable can depend on its latent memory state through a random lag (rather than a fixed lag), thus modeling memory recall with differing lags at distinct times. Under this setting, we develop an estimator and prove that under a genericity assumption, the parameters of the model can be learned consistently. We also propose a practical adaption of this estimator, which demonstrates significant performance gains in both synthetic and real-world datasets.

Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find stationary points of the likelihood objective, and these points may be far from any maximizer. This article addresses this disconnect between the statistical principles behind EM and its algorithmic properties. Specifically, it provides a global analysis of EM for specific models in which the observations comprise an i.i.d. sample from a mixture of two Gaussians. This is achieved by (i) studying the sequence of parameters from idealized execution of EM in the infinite sample limit, and fully characterizing the limit points of the sequence in terms of the initial parameters; and then (ii) based on this convergence analysis, establishing statistical consistency (or lack thereof) for the actual sequence of parameters produced by EM.

This becomes even more problematic with highly articulated modern prostheses. The natural use of these devices is challenging in everyday life primarily due to the software [2, 3, 4]. The open question is how to reduce this training time while making control as natural as possible. Machine learning has opened a new path to tackle this problem by allowing the prosthesis to adapt to the myoelectric signals of a specific user. Although these methods have been applied with success (e.g., [5] and references therein), they still require a significant amount of data from individual subjects to learn models with satisfactory performance. Consider a situation in which different subjects repeat the same hand postures and suppose that a new target user attempts to learn the same movements. In this case it should be beneficial to reuse the information from the latter subjects and thereby reduce the training data required from a new subject. However, even if a movement appears the same for all subjects, the distribution of their myoelectric signals is very different.

The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilizing a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimator leads to the well-known unscented Kalman filter (UKF). Although the UKF works very well in Gaussian noises, its performance may deteriorate significantly when the noises are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises. To improve the robustness of the UKF against impulsive noises, a new filter for nonlinear systems is proposed in this work, namely the maximum correntropy unscented filter (MCUF). In MCUF, the UT is applied to obtain the prior estimates of the state and covariance matrix, and a robust statistical linearization regression based on the maximum correntropy criterion (MCC) is then used to obtain the posterior estimates of the state and covariance. The satisfying performance of the new algorithm is confirmed by two illustrative examples.

It is well-known that the precision of data, hyperparameters, and internal representations employed in learning systems directly impacts its energy, throughput, and latency. The precision requirements for the training algorithm are also important for systems that learn on-the-fly. Prior work has shown that the data and hyperparameters can be quantized heavily without incurring much penalty in classification accuracy when compared to floating point implementations. These works suffer from two key limitations. First, they assume uniform precision for the classifier and for the training algorithm and thus miss out on the opportunity to further reduce precision. Second, prior works are empirical studies. In this article, we overcome both these limitations by deriving analytical lower bounds on the precision requirements of the commonly employed stochastic gradient descent (SGD) on-line learning algorithm in the specific context of a support vector machine (SVM). Lower bounds on the data precision are derived in terms of the the desired classification accuracy and precision of the hyperparameters used in the classifier. Additionally, lower bounds on the hyperparameter precision in the SGD training algorithm are obtained. These bounds are validated using both synthetic and the UCI breast cancer dataset. Additionally, the impact of these precisions on the energy consumption of a fixed-point SVM with on-line training is studied.

In this paper, we address the problem of conditional modality learning, whereby one is interested in generating one modality given the other. While it is straightforward to learn a joint distribution over multiple modalities using a deep multimodal architecture, we observe that such models aren't very effective at conditional generation. Hence, we address the problem by learning conditional distributions between the modalities. We use variational methods for maximizing the corresponding conditional log-likelihood. The resultant deep model, which we refer to as conditional multimodal autoencoder (CMMA), forces the latent representation obtained from a single modality alone to be `close' to the joint representation obtained from multiple modalities. We use the proposed model to generate faces from attributes. We show that the faces generated from attributes using the proposed model, are qualitatively and quantitatively more representative of the attributes from which they were generated, than those obtained by other deep generative models. We also propose a secondary task, whereby the existing faces are modified by modifying the corresponding attributes. We observe that the modifications in face introduced by the proposed model are representative of the corresponding modifications in attributes.

While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the natural structure of ensemble learners like bagged trees and random forests has been shown to admit desirable asymptotic properties when base learners are built with proper subsamples. In this work, we demonstrate that by defining an appropriate grid structure on the covariate space, we may carry out formal hypothesis tests for both variable importance and underlying additive model structure. To our knowledge, these tests represent the first statistical tools for investigating the underlying regression structure in a context such as random forests. We develop notions of total and partial additivity and further demonstrate that testing can be carried out at no additional computational cost by estimating the variance within the process of constructing the ensemble. Furthermore, we propose a novel extension of these testing procedures utilizing random projections in order to allow for computationally efficient testing procedures that retain high power even when the grid size is much larger than that of the training set.

Research on Offline Handwritten Signature Verification explored a large variety of handcrafted feature extractors, ranging from graphology, texture descriptors to interest points. In spite of advancements in the last decades, performance of such systems is still far from optimal when we test the systems against skilled forgeries - signature forgeries that target a particular individual. In previous research, we proposed a formulation of the problem to learn features from data (signature images) in a Writer-Independent format, using Deep Convolutional Neural Networks (CNNs), seeking to improve performance on the task. In this research, we push further the performance of such method, exploring a range of architectures, and obtaining a large improvement in state-of-the-art performance on the GPDS dataset, the largest publicly available dataset on the task. In the GPDS-160 dataset, we obtained an Equal Error Rate of 2.74%, compared to 6.97% in the best result published in literature (that used a combination of multiple classifiers). We also present a visual analysis of the feature space learned by the model, and an analysis of the errors made by the classifier. Our analysis shows that the model is very effective in separating signatures that have a different global appearance, while being particularly vulnerable to forgeries that very closely resemble genuine signatures, even if their line quality is bad, which is the case of slowly-traced forgeries.

The amount of digitally available but heterogeneous information about the world is remarkable, and new technologies such as self-driving cars, smart homes, or the internet of things may further increase it. In this paper we examine certain aspects of the problem of how such heterogeneous information can be harnessed by autonomous agents. After discussing potentials and limitations of some existing approaches, we investigate how \emph{experiments} can help to obtain a better understanding of the problem. Specifically, we present a simple agent that integrates video data from a different agent, and implement and evaluate a version of it on the novel experimentation platform \emph{Malmo}. The focus of a second investigation is on how information about the hardware of different agents, the agents' sensory data, and \emph{causal} information can be utilized for knowledge transfer between agents and subsequently more data-efficient decision making. Finally, we discuss potential future steps w.r.t.\ theory and experimentation, and formulate open questions.