Estimating causal effects in the presence of latent confounding is a frequently occurring problem in several tasks. In real world applications such as medicine, accounting for the effects of latent confounding is even more challenging as a result of high-dimensional and noisy data. In this work, we propose estimating the causal effect from the perspective of the information bottleneck principle by explicitly identifying a low-dimensional representation of latent confounding. In doing so, we prove theoretically that the proposed model can be used to recover the average causal effect. Experiments on both synthetic data and existing causal benchmarks illustrate that our method achieves state-of-the-art performance in terms of prediction accuracy and sample efficiency, without sacrificing interpretability.

The problem of recognizing actions or activities has been widely addressed in the computer vision research community: it consists in the classification of a fully or partially observed action, typically observed through cameras or external motion capture [2]. In robotics, recognizing the human activity is paramount for enabling a proper interaction and providing assistance to the human: an assistive device or prosthetics could switch control modes depending on the current human activity (e.g., walking or sitting) [3], [4]; a mobile robot may adapt its navigation depending on the prediction of the human motion [5]. More generally, prediction is important to provide the robot with anticipation capabilities [6]. In collaborative robotics applications in manufacturing, such as in assembly lines, recognizing the current activity of the operator is necessary for ergonomics evaluations [7] and for the optimization of the robot actions. However, there are two critical issues that prevent the direct application of existing techniques in such scenarios. The first issue is the availability of external sensing devices (cameras or motion captures) that poses constraints on the application for many tasks and application scenarios.

Alzheimer's disease is the most common dementia leading to an irreversible neurodegenerative process. To date, subject revealed advanced brain structural alterations when the diagnosis is established. Therefore, an earlier diagnosis of this dementia is crucial although it is a challenging task. Recently, many studies have proposed biomarkers to perform early detection of Alzheimer's disease. Some of them have proposed methods based on inter-subject similarity while other approaches have investigated framework using intra-subject variability. In this work, we propose a novel framework combining both approaches within an efficient graph of brain structures grading. Subsequently, we demonstrate the competitive performance of the proposed method compared to state-of-the-art methods.

Unsupervised domain adaptation techniques have been successful for a wide range of problems where supervised labels are limited. The task is to classify an unlabeled `target' dataset by leveraging a labeled `source' dataset that comes from a slightly similar distribution. We propose metric-based adversarial discriminative domain adaptation (M-ADDA) which performs two main steps. First, it uses a metric learning approach to train the source model on the source dataset by optimizing the triplet loss function. This results in clusters where embeddings of the same label are close to each other and those with different labels are far from one another. Next, it uses the adversarial approach (as that used in ADDA \cite{2017arXiv170205464T}) to make the extracted features from the source and target datasets indistinguishable. Simultaneously, we optimize a novel loss function that encourages the target dataset's embeddings to form clusters. While ADDA and M-ADDA use similar architectures, we show that M-ADDA performs significantly better on the digits adaptation datasets of MNIST and USPS. This suggests that using metric-learning for domain adaptation can lead to large improvements in classification accuracy for the domain adaptation task. The code is available at \url{https://github.com/IssamLaradji/M-ADDA}.

Centroid-based methods including k-means and fuzzy c-means are known as effective and easy-to-implement approaches to clustering purposes in many areas of application. However, these algorithms cannot be directly applied to supervised tasks. We propose a generative model extending centroid-based clustering approaches to be applicable to classification tasks. Given an arbitrary loss function, our approach, termed Supervised Fuzzy Partitioning (SFP), incorporates labels information into its objective function through a surrogate term penalizing the risk. We also fuzzify the partition and assign weights to features alongside entropy-based regularization terms, enabling the method to capture more complex data structure, to identify significant features, and to yield better performance facing high-dimensional data. An iterative algorithm based on block coordinate descent scheme was formulated to efficiently find a local optimizer. The results show that the SFP performance in classification of ultra high-dimensional gene expression data is competitive with state-of-the-art algorithms such as random forest and SVM. Our method has a major advantage over such methods in that it not only leads to a flexible model suitable for high-dimensional cases but also uses the loss function in training phase without compromising computational efficiency.

Estimating a large alphabet probability distribution from a limited number of samples is a fundamental problem in machine learning and statistics. A variety of estimation schemes have been proposed over the years, mostly inspired by the early work of Laplace and the seminal contribution of Good and Turing. One of the basic assumptions shared by most commonly-used estimators is the unique correspondence between the symbol's sample frequency and its estimated probability. In this work we tackle this paradigmatic assumption; we claim that symbols with "similar" frequencies shall be assigned the same estimated probability value. This way we regulate the number of parameters and improve generalization. In this preliminary report we show that by applying an ensemble of such regulated estimators, we introduce a dramatic enhancement in the estimation accuracy (typically up to 50%), compared to currently known methods. An implementation of our suggested method is publicly available at the first author's web-page.

This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two essentially separate communities, and this makes it difficult to seamlessly transfer results between them. Our aim is to overcome this potential difficulty. To this end, we review several old and new results and concepts from either side, and juxtapose algorithmic quantities from each framework to highlight close similarities. We also provide discussions on subtle philosophical and theoretical differences between the two approaches.

Self-paced learning (SPL) mimics the cognitive process of humans, who generally learn from easy samples to hard ones. One key issue in SPL is the training process required for each instance weight depends on the other samples and thus cannot easily be run in a distributed manner in a large-scale dataset. In this paper, we reformulate the self-paced learning problem into a distributed setting and propose a novel Distributed Self-Paced Learning method (DSPL) to handle large-scale datasets. Specifically, both the model and instance weights can be optimized in parallel for each batch based on a consensus alternating direction method of multipliers. We also prove the convergence of our algorithm under mild conditions. Extensive experiments on both synthetic and real datasets demonstrate that our approach is superior to those of existing methods.

We introduce a kernel approximation strategy that enables computation of the Gaussian process log marginal likelihood and all hyperparameter derivatives in $\mathcal{O}(p)$ time. Our GRIEF kernel consists of $p$ eigenfunctions found using a Nystr\"om approximation from a dense Cartesian product grid of inducing points. By exploiting algebraic properties of Kronecker and Khatri-Rao tensor products, computational complexity of the training procedure can be practically independent of the number of inducing points. This allows us to use arbitrarily many inducing points to achieve a globally accurate kernel approximation, even in high-dimensional problems. The fast likelihood evaluation enables type-I or II Bayesian inference on large-scale datasets. We benchmark our algorithms on real-world problems with up to two-million training points and $10^{33}$ inducing points.

Dropout, a stochastic regularisation technique for training of neural networks, has recently been reinterpreted as a specific type of approximate inference algorithm for Bayesian neural networks. The main contribution of the reinterpretation is in providing a theoretical framework useful for analysing and extending the algorithm. We show that the proposed framework suffers from several issues; from undefined or pathological behaviour of the true posterior related to use of improper priors, to an ill-defined variational objective due to singularity of the approximating distribution relative to the true posterior. Our analysis of the improper log uniform prior used in variational Gaussian dropout suggests the pathologies are generally irredeemable, and that the algorithm still works only because the variational formulation annuls some of the pathologies. To address the singularity issue, we proffer Quasi-KL (QKL) divergence, a new approximate inference objective for approximation of high-dimensional distributions. We show that motivations for variational Bernoulli dropout based on discretisation and noise have QKL as a limit. Properties of QKL are studied both theoretically and on a simple practical example which shows that the QKL-optimal approximation of a full rank Gaussian with a degenerate one naturally leads to the Principal Component Analysis solution.