Deep neural networks are representation learning techniques. During training, a deep net is capable of generating a descriptive language of unprecedented size and detail in machine learning. Extracting the descriptive language coded within a trained CNN model (in the case of image data), and reusing it for other purposes is a field of interest, as it provides access to the visual descriptors previously learnt by the CNN after processing millions of images, without requiring an expensive training phase. Contributions to this field (commonly known as feature representation transfer or transfer learning) have been purely empirical so far, extracting all CNN features from a single layer close to the output and testing their performance by feeding them to a classifier. This approach has provided consistent results, although its relevance is limited to classification tasks. In a completely different approach, in this paper we statistically measure the discriminative power of every single feature found within a deep CNN, when used for characterizing every class of 11 datasets. We seek to provide new insights into the behavior of CNN features, particularly the ones from convolutional layers, as this can be relevant for their application to knowledge representation and reasoning. Our results confirm that low and middle level features may behave differently to high level features, but only under certain conditions. We find that all CNN features can be used for knowledge representation purposes both by their presence or by their absence, doubling the information a single CNN feature may provide. We also study how much noise these features may include, and propose a thresholding approach to discard most of it. All these insights have a direct application to the generation of CNN embedding spaces.

Data efficiency, i.e., learning from small data sets, is critical in many practical applications where data collection is time consuming or expensive, e.g., robotics, animal experiments or drug design. Meta learning is one way to increase the data efficiency of learning algorithms by generalizing learned concepts from a set of training tasks to unseen, but related, tasks. Often, this relationship between tasks is hard coded or relies in some other way on human expertise. In this paper, we propose to automatically learn the relationship between tasks using a latent variable model. Our approach finds a variational posterior over tasks and averages over all plausible (according to this posterior) tasks when making predictions. We apply this framework within a model-based reinforcement learning setting for learning dynamics models and controllers of many related tasks. We apply our framework in a model-based reinforcement learning setting, and show that our model effectively generalizes to novel tasks, and that it reduces the average interaction time needed to solve tasks by up to 60% compared to strong baselines.

Issues regarding explainable AI involve four components: users, laws & regulations, explanations and algorithms. Together these components provide a context in which explanation methods can be evaluated regarding their adequacy. The goal of this chapter is to bridge the gap between expert users and lay users. Different kinds of users are identified and their concerns revealed, relevant statements from the General Data Protection Regulation are analyzed in the context of Deep Neural Networks (DNNs), a taxonomy for the classification of existing explanation methods is introduced, and finally, the various classes of explanation methods are analyzed to verify if user concerns are justified. Overall, it is clear that (visual) explanations can be given about various aspects of the influence of the input on the output. However, it is noted that explanation methods or interfaces for lay users are missing and we speculate which criteria these methods / interfaces should satisfy. Finally it is noted that two important concerns are difficult to address with explanation methods: the concern about bias in datasets that leads to biased DNNs, as well as the suspicion about unfair outcomes.

We analyze two novel randomized variants of the Frank-Wolfe (FW) or conditional gradient algorithm. While classical FW algorithms require solving a linear minimization problem over the domain at each iteration, the proposed method only requires to solve a linear minimization problem over a small \emph{subset} of the original domain. The first algorithm that we propose is a randomized variant of the original FW algorithm and achieves a $\mathcal{O}(1/t)$ sublinear convergence rate as in the deterministic counterpart. The second algorithm is a randomized variant of the Away-step FW algorithm, and again as its deterministic counterpart, reaches linear (i.e., exponential) convergence rate making it the first provably convergent randomized variant of Away-step FW. In both cases, while subsampling reduces the convergence rate by a constant factor, the linear minimization step can be a fraction of the cost of that of the deterministic versions, especially when the data is streamed. We illustrate computational gains of the algorithms on regression problems, involving both $\ell_1$ and latent group lasso penalties.

Gaussian processes are a natural extension of the ubiquitous kernel regression to the Bayesian setting where the regression parameters are modelled as random variables with a Gaussian prior distribution [1]. Given the training observations, Gaussian processes generate posterior probabilities of the target or output for new inputs or observations, as a function of the training data and the input kernel function [2]. Gaussian process models and its variants have been applied in a number of diverse fields such as model predictive control and system analysis [3]-[7], latent variable models [8]-[11], multi-task learning [10], [12], [13], image analysis and synthesis [14]- [17], speech processing [18]-[20], and magnetic resonance imaging (MRI) [21], [22]. Gaussian processes have also been extended to a non-stationary regression setting [23]-[25] and for regression over complex-valued data [26]. Recently, Gaussian processes were shown to be useful in training and analysis of deep neural networks, and that a Gaussian process can be viewed as a neural network with a single infinite-dimensional layer of hidden units [27], [28].

Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable, leading to extensive study of approximation methods. Iterative variational methods are a popular and successful family of approaches. However, even state of the art variational methods can return poor results or fail to converge on difficult instances. In this paper, we instead consider computing the partition function via sequential summation over variables. We develop robust approximate algorithms by combining ideas from mini-bucket elimination with tensor network and renormalization group methods from statistical physics. The resulting "convergence-free" methods show good empirical performance on both synthetic and real-world benchmark models, even for difficult instances.

In this paper, we describe a solution to tackle a common set of challenges in e-commerce, which arise from the fact that new products are continually being added to the catalogue. The challenges involve properly personalising the customer experience, forecasting demand and planning the product range. We argue that the foundational piece to solve all of these problems is having consistent and detailed information about each product, information that is rarely available or consistent given the multitude of suppliers and types of products. We describe in detail the architecture and methodology implemented at ASOS, one of the world's largest fashion e-commerce retailers, to tackle this problem. We then show how this quantitative understanding of the products can be leveraged to improve recommendations in a hybrid recommender system approach.

The central aim in this paper is to address variable selection questions in nonlinear and nonparametric regression. Motivated by statistical genetics, where nonlinear interactions are of particular interest, we introduce a novel, interpretable, and computationally efficient way to summarize the relative importance of predictor variables. Methodologically, we develop the "RelATive cEntrality" (RATE) measure to prioritize candidate genetic variants that are not just marginally important, but whose associations also stem from significant covarying relationships with other variants in the data. We illustrate RATE through Bayesian Gaussian process regression, but the methodological innovations apply to other nonlinear methods. It is known that nonlinear models often exhibit greater predictive accuracy than linear models, particularly for phenotypes generated by complex genetic architectures. With detailed simulations and an Arabidopsis thaliana QTL mapping study, we show that applying RATE enables an explanation for this improved performance.

Unsupervised Domain Adaptation (DA) is used to automatize the task of labeling data: an unlabeled dataset (target) is annotated using a labeled dataset (source) from a related domain. We cast domain adaptation as the problem of finding stable labels for target examples. A new definition of label stability is proposed, motivated by a generalization error bound for large margin linear classifiers: a target labeling is stable when, with high probability, a classifier trained on a random subsample of the target with that labeling yields the same labeling. We find stable labelings using a random walk on a directed graph with transition probabilities based on labeling stability. The majority vote of those labelings visited by the walk yields a stable label for each target example. The resulting domain adaptation algorithm is strikingly easy to implement and apply: It does not rely on data transformations, which are in general computational prohibitive in the presence of many input features, and does not need to access the source data, which is advantageous when data sharing is restricted. By acting on the original feature space, our method is able to take full advantage of deep features from external pre-trained neural networks, as demonstrated by the results of our experiments.

In this paper, we deal with the problem of inferring causal directions when the data is on discrete domain. By considering the distribution of the cause $P(X)$ and the conditional distribution mapping cause to effect $P(Y|X)$ as independent random variables, we propose to infer the causal direction via comparing the distance correlation between $P(X)$ and $P(Y|X)$ with the distance correlation between $P(Y)$ and $P(X|Y)$. We infer "$X$ causes $Y$" if the dependence coefficient between $P(X)$ and $P(Y|X)$ is smaller. Experiments are performed to show the performance of the proposed method.