The positivity assumption, or the experimental treatment assignment (ETA) assumption, is important for identifiability in causal inference. Even if the positivity assumption holds, practical violations of this assumption may jeopardize the finite sample performance of the causal estimator. One of the consequences of practical violations of the positivity assumption is extreme values in the estimated propensity score (PS). A common practice to address this issue is truncating the PS estimate when constructing PS-based estimators. In this study, we propose a novel adaptive truncation method, Positivity-C-TMLE, based on the collaborative targeted maximum likelihood estimation (C-TMLE) methodology. We demonstrate the outstanding performance of our novel approach in a variety of simulations by comparing it with other commonly studied estimators. Results show that by adaptively truncating the estimated PS with a more targeted objective function, the Positivity-C-TMLE estimator achieves the best performance for both point estimation and confidence interval coverage among all estimators considered.

In this paper we are interested in the problem of learning an over-complete basis and a methodology such that the reconstruction or inverse problem does not need optimization. We analyze the optimality of the presented approaches, their link to popular already known techniques s.a. Artificial Neural Networks,k-means or Oja's learning rule. Finally, we will see that one approach to reach the optimal dictionary is a factorial and hierarchical approach. The derived approach lead to a formulation of a Deep Oja Network. We present results on different tasks and present the resulting very efficient learning algorithm which brings a new vision on the training of deep nets. Finally, the theoretical work shows that deep frameworks are one way to efficiently have over-complete (combinatorially large) dictionary yet allowing easy reconstruction. We thus present the Deep Residual Oja Network (DRON). We demonstrate that a recursive deep approach working on the residuals allow exponential decrease of the error w.r.t. the depth.

The pairwise influence matrix of Dobrushin has long been used as an analytical tool to bound the rate of convergence of Gibbs sampling. In this work, we use Dobrushin influence as the basis of a practical tool to certify and efficiently improve the quality of a discrete Gibbs sampler. Our Dobrushin-optimized Gibbs samplers (DoGS) offer customized variable selection orders for a given sampling budget and variable subset of interest, explicit bounds on total variation distance to stationarity, and certifiable improvements over the standard systematic and uniform random scan Gibbs samplers. In our experiments with joint image segmentation and object recognition, Markov chain Monte Carlo maximum likelihood estimation, and Ising model inference, DoGS consistently deliver higher-quality inferences with significantly smaller sampling budgets than standard Gibbs samplers.

Generative Adversarial Networks (GANs) have been shown to be able to sample impressively realistic images. GAN training consists of a saddle point optimization problem that can be thought of as an adversarial game between a generator which produces the images, and a discriminator, which judges if the images are real. Both the generator and the discriminator are commonly parametrized as deep convolutional neural networks. The goal of this paper is to disentangle the contribution of the optimization procedure and the network parametrization to the success of GANs. To this end we introduce and study Generative Latent Optimization (GLO), a framework to train a generator without the need to learn a discriminator, thus avoiding challenging adversarial optimization problems. We show experimentally that GLO enjoys many of the desirable properties of GANs: learning from large data, synthesizing visually-appealing samples, interpolating meaningfully between samples, and performing linear arithmetic with noise vectors.

Bayesian optimization has recently attracted the attention of the automatic machine learning community for its excellent results in hyperparameter tuning. BO is characterized by the sample efficiency with which it can optimize expensive black-box functions. The efficiency is achieved in a similar fashion to the learning to learn methods: surrogate models (typically in the form of Gaussian processes) learn the target function and perform intelligent sampling. This surrogate model can be applied even in the presence of noise; however, as with most regression methods, it is very sensitive to outlier data. This can result in erroneous predictions and, in the case of BO, biased and inefficient exploration. In this work, we present a GP model that is robust to outliers which uses a Student-t likelihood to segregate outliers and robustly conduct Bayesian optimization. We present numerical results evaluating the proposed method in both artificial functions and real problems.

Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the application domain. If this is not possible, the data structure has to be inferred from the mere signal observations. This is exactly the problem that we address in this paper, under the assumption that the graph signals can be represented as a sparse linear combination of a few atoms of a structured graph dictionary. The dictionary is constructed on polynomials of the graph Laplacian, which can sparsely represent a general class of graph signals composed of localized patterns on the graph. We formulate a graph learning problem, whose solution provides an ideal fit between the signal observations and the sparse graph signal model. As the problem is non-convex, we propose to solve it by alternating between a signal sparse coding and a graph update step. We provide experimental results that outline the good graph recovery performance of our method, which generally compares favourably to other recent network inference algorithms.

We consider the task of one-shot learning of visual categories, or more generally, learning to classify images with few examples of particular classes. The currently dominant image classification paradigm of supervised deep learning performs well only when data is abundant. In this paper we explore a Bayesian procedure for updating a pretrained convnet to classify a novel image category for which data is limited. We demonstrate that the approach is competitive with state-of-the-art methods whilst also being consistent with'normal' methods for training deep networks on large data. Several approaches to one-shot learning have been noted as failing to beat a simple nearest-neighbour classifier [8]. Recent approaches of the problem have used relatively complicated architectures such as memory augmented neural networks [9, 10] or siamese networks [5]; or have been specialised for the task of one-shot learning [10]. Fei-Fei et al. [2] demonstrated one-shot learning as a Bayesian update to an image classification model with a prior based on categories learned with lots of data. Our work is an modern update of this work, applying this technique to deep convolutional networks.

Much work has been done in understanding human creativity and defining measures to evaluate creativity. This is necessary mainly for the reason of having an objective and automatic way of quantifying creative artifacts. In this work, we propose a regression-based learning framework which takes into account quantitatively the essential criteria for creativity like novelty, influence, value and unexpectedness. As it is often the case with most creative domains, there is no clear ground truth available for creativity. Our proposed learning framework is applicable to all creative domains; yet we evaluate it on a dataset of movies created from IMDb and Rotten Tomatoes due to availability of audience and critic scores, which can be used as proxy ground truth labels for creativity. We report promising results and observations from our experiments in the following ways : 1) Correlation of creative criteria with critic scores, 2) Improvement in movie rating prediction with inclusion of various creative criteria, and 3) Identification of creative movies.

We investigate the problems of identity and closeness testing over a discrete population from random samples. Our goal is to develop efficient testers while guaranteeing Differential Privacy to the individuals of the population. We describe an approach that yields sample-efficient differentially private testers for these problems. Our theoretical results show that there exist private identity and closeness testers that are nearly as sample-efficient as their non-private counterparts. We perform an experimental evaluation of our algorithms on synthetic data. Our experiments illustrate that our private testers achieve small type I and type II errors with sample size sublinear in the domain size of the underlying distributions.

We demonstrate the potential of Deep Learning methods for measurements of cosmological parameters from density fields, focusing on the extraction of non-Gaussian information. We consider weak lensing mass maps as our dataset. We aim for our method to be able to distinguish between five models, which were chosen to lie along the $\sigma_8$ - $\Omega_m$ degeneracy, and have nearly the same two-point statistics. We design and implement a Deep Convolutional Neural Network (DCNN) which learns the relation between five cosmological models and the mass maps they generate. We develop a new training strategy which ensures the good performance of the network for high levels of noise. We compare the performance of this approach to commonly used non-Gaussian statistics, namely the skewness and kurtosis of the convergence maps. We find that our implementation of DCNN outperforms the skewness and kurtosis statistics, especially for high noise levels. The network maintains the mean discrimination efficiency greater than $85\%$ even for noise levels corresponding to ground based lensing observations, while the other statistics perform worse in this setting, achieving efficiency less than $70\%$. This demonstrates the ability of CNN-based methods to efficiently break the $\sigma_8$ - $\Omega_m$ degeneracy with weak lensing mass maps alone. We discuss the potential of this method to be applied to the analysis of real weak lensing data and other datasets.