Meta-learning consists in learning learning algorithms. We use a Long Short Term Memory (LSTM) based network to learn to compute on-line updates of the parameters of another neural network. These parameters are stored in the cell state of the LSTM. Our framework allows to compare learned algorithms to hand-made algorithms within the traditional train and test methodology. In an experiment, we learn a learning algorithm for a one-hidden layer Multi-Layer Perceptron (MLP) on non-linearly separable datasets. The learned algorithm is able to update parameters of both layers and generalise well on similar datasets.

We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable $X$ lead to consistent estimators of the mean embedding of $f(X)$. For Mat\'ern kernels and sufficiently smooth functions we also provide rates of convergence. Our results extend to functions of multiple random variables. If the variables are dependent, we require an estimator of the mean embedding of their joint distribution as a starting point; if they are independent, it is sufficient to have separate estimators of the mean embeddings of their marginal distributions. In either case, our results cover both mean embeddings based on i.i.d. samples as well as "reduced set" expansions in terms of dependent expansion points. The latter serves as a justification for using such expansions to limit memory resources when applying the approach as a basis for probabilistic programming.

While most of these algorithms have polynomial-time complexity, determinantal point processes are too slow in practice for large number N of items to choose a subset from. Simplest algorithms have cubic running-time complexity and do not scale well to more than N 1000. Some progress has been made recently to reach quadratic or linear time complexity in N when imposing low-rank constraints, for both learning and inference [Mariet and Sra, 2016, Gartrell et al., 2016]. This is not enough, in particular for applications in continuous DPPs where the base set is infinite, and for modelling documents as a subset of all possible sentences: the number of sentences, even taken with a bag-of-word assumption, scales exponentially with the vocabulary size. Our goal in this paper is to design a class of DPPs which can be manipulated (for inference and parameter learning) in potentially sublinear time in the number of items N. In order to circumvent even linear-time complexity, we consider a novel class of DPPs which relies on a particular low-rank decomposition of the associated positive definite matrices.

In the matrix completion problem, we seek to recover or estimate a matrix, when only a fraction of its entries are observed. While it is impossible to complete an arbitrary matrix using only partial observations of its entries, it may be possible to fully recover matrix entries when the matrix has an appropriate underlying structure. For example, most low-rank matrices can be completed accurately with high probability, by solving a convex optimization problem (Candés and Recht, 2009). Consequently, algorithms for lowrank matrix completion have enjoyed widespread use across many disciplines, including collaborative filtering and recommender systems (Koren et al., 2009), multi-task learning and classification (Amit et al., 2007; Argyriou et al., 2007; Wu and Lange, 2015), computer vision (Chen and Suter, 2004), statistical genetics (Chi et al., 2013), as well as remote sensing (Malek-Mohammadi et al., 2014). In this paper, we consider matrix completion under a structural assumption that is closely related to the low-rank assumption; i.e., we assume that the matrix entries vary "smoothly" with respect to a graphical organization of the rows and columns. For example, in the context of a movie recommendation system, we seek to complete a user-by-movies ratings matrix. We may have additional information about users, such as if pairs of users are friends on a social media application, as well as additional information from a movie database, such as the co-occurrence of certain film principles. We expect the entries of a movie ratings matrix to vary "smoothly" over a neighborhood of users, defined by a friendship graph, and over a neighborhood of movies, defined by a shared movie principles graph. When such local similarity structure exists, and is available, it behooves us to leverage this information to predict missing entries in a matrix.

The reparameterization gradient has become a widely used method to obtain Monte Carlo gradients to optimize the variational objective. However, this technique does not easily apply to commonly used distributions such as beta or gamma without further approximations, and most practical applications of the reparameterization gradient fit Gaussian distributions. In this paper, we introduce the generalized reparameterization gradient, a method that extends the reparameterization gradient to a wider class of variational distributions. Generalized reparameterizations use invertible transformations of the latent variables which lead to transformed distributions that weakly depend on the variational parameters. This results in new Monte Carlo gradients that combine reparameterization gradients and score function gradients. We demonstrate our approach on variational inference for two complex probabilistic models. The generalized reparameterization is effective: even a single sample from the variational distribution is enough to obtain a low-variance gradient.

In this paper we study the problem of exact recovery of the pure-strategy Nash equilibria (PSNE) set of a graphical game from noisy observations of joint actions of the players alone. We consider sparse linear influence games --- a parametric class of graphical games with linear payoffs, and represented by directed graphs of n nodes (players) and in-degree of at most k. We present an $\ell_1$-regularized logistic regression based algorithm for recovering the PSNE set exactly, that is both computationally efficient --- i.e. runs in polynomial time --- and statistically efficient --- i.e. has logarithmic sample complexity. Specifically, we show that the sufficient number of samples required for exact PSNE recovery scales as $\mathcal{O}(\mathrm{poly}(k) \log n)$. We also validate our theoretical results using synthetic experiments.

We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of sparsity across precision matrices. It gives sparse estimates of interactions and produces interpretable models. Inspired by the connected-components structure of the estimated precision matrices, we propose the community Bayes model, which partitions features into several conditional independent communities and splits the classification problem into separate smaller ones. The community Bayes idea is quite general and can be applied to non-Gaussian data and likelihood-based classifiers.

A major hurdle to clinical translation of brain-machine interfaces (BMIs) is that current decoders, which are trained from a small quantity of recent data, become ineffective when neural recording conditions subsequently change. We tested whether a decoder could be made more robust to future neural variability by training it to handle a variety of recording conditions sampled from months of previously collected data as well as synthetic training data perturbations. We developed a new multiplicative recurrent neural network BMI decoder that successfully learned a large variety of neural-to- kinematic mappings and became more robust with larger training datasets. When tested with a non-human primate preclinical BMI model, this decoder was robust under conditions that disabled a state-of-the-art Kalman filter based decoder. These results validate a new BMI strategy in which accumulated data history is effectively harnessed, and may facilitate reliable daily BMI use by reducing decoder retraining downtime.

The human face constantly conveys information, both consciously and subconsciously. However, as basic as it is for humans to visually interpret this information, it is quite a big challenge for machines. Conventional semantic facial feature recognition and analysis techniques are already in use and are based on physiological heuristics, but they suffer from lack of robustness and high computation time. This thesis aims to explore ways for machines to learn to interpret semantic information available in faces in an automated manner without requiring manual design of feature detectors, using the approach of Deep Learning. This thesis provides a study of the effects of various factors and hyper-parameters of deep neural networks in the process of determining an optimal network configuration for the task of semantic facial feature recognition. This thesis explores the effectiveness of the system to recognize the various semantic features (like emotions, age, gender, ethnicity etc.) present in faces. Furthermore, the relation between the effect of high-level concepts on low level features is explored through an analysis of the similarities in low-level descriptors of different semantic features. This thesis also demonstrates a novel idea of using a deep network to generate 3-D Active Appearance Models of faces from real-world 2-D images. For a more detailed report on this work, please see [arXiv:1512.00743v1].

This paper explores the capabilities of convolutional neural networks to deal with a task that is easily manageable for humans: perceiving 3D pose of a human body from varying angles. However, in our approach, we are restricted to using a monocular vision system. For this purpose, we apply a convolutional neural network approach on RGB videos and extend it to three dimensional convolutions. This is done via encoding the time dimension in videos as the 3\ts{rd} dimension in convolutional space, and directly regressing to human body joint positions in 3D coordinate space. This research shows the ability of such a network to achieve state-of-the-art performance on the selected Human3.6M dataset, thus demonstrating the possibility of successfully representing temporal data with an additional dimension in the convolutional operation.