Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate the usefulness of different notions of disentanglement for improving the fairness of downstream prediction tasks based on representations. We consider the setting where the goal is to predict a target variable based on the learned representation of high-dimensional observations (such as images) that depend on both the target variable and an unobserved sensitive variable. We show that in this setting both the optimal and empirical predictions can be unfair, even if the target variable and the sensitive variable are independent. Analyzing more than 12 600 trained representations of state-of-the-art disentangled models, we observe that various disentanglement scores are consistently correlated with increased fairness, suggesting that disentanglement may be a useful property to encourage fairness when sensitive variables are not observed.

We propose subspace networks for the problem of few-shot classification, where a classifier must generalize to new classes not seen in the training set, given only a small number of examples of each class. Subspace networks learn an embedding space in which classification can be performed by computing distances of embedded points to subspace representations of each class. The class subspaces are spanned by examples belonging to the same class, transformed by a learnable embedding function. Similarly to recent approaches for few-shot learning, subspace networks reflect a simple inductive bias that is beneficial in this limited-data regime and they achieve excellent results. In particular, our proposed method shows consistently better performance than other state-of-the-art few-shot distance-metric learning methods when the embedding function is deep or when training and testing domains are shifted.

Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on the Tucker factorisation of tensors. The probabilistic interpretation of such approximation allows us to define a new probabilistic model for tree-structured data. Hence, we define the new approximated model and we derive its learning algorithm. Then, we empirically assess the effective power of the new model evaluating it on two different tasks. In both cases, our model outperforms the other approximated model known in the literature.

We study the complexity of sampling from a distribution over all index subsets of the set $\{1,...,n\}$ with the probability of a subset $S$ proportional to the determinant of the submatrix $\mathbf{L}_S$ of some $n\times n$ p.s.d. matrix $\mathbf{L}$, where $\mathbf{L}_S$ corresponds to the entries of $\mathbf{L}$ indexed by $S$. Known as a determinantal point process, this distribution is used in machine learning to induce diversity in subset selection. In practice, we often wish to sample multiple subsets $S$ with small expected size $k = E[|S|] \ll n$ from a very large matrix $\mathbf{L}$, so it is important to minimize the preprocessing cost of the procedure (performed once) as well as the sampling cost (performed repeatedly). For this purpose, we propose a new algorithm which, given access to $\mathbf{L}$, samples exactly from a determinantal point process while satisfying the following two properties: (1) its preprocessing cost is $n \cdot \text{poly}(k)$, i.e., sublinear in the size of $\mathbf{L}$, and (2) its sampling cost is $\text{poly}(k)$, i.e., independent of the size of $\mathbf{L}$. Prior to our results, state-of-the-art exact samplers required $O(n^3)$ preprocessing time and sampling time linear in $n$ or dependent on the spectral properties of $\mathbf{L}$. We also give a reduction which allows using our algorithm for exact sampling from cardinality constrained determinantal point processes with $n\cdot\text{poly}(k)$ time preprocessing.

The goal of dynamic time warping is to transform or warp time in order to approximately align two signals together. We pose the choice of warping function as an optimization problem with several terms in the objective. The first term measures the misalignment of the time-warped signals. Two additional regularization terms penalize the cumulative warping and the instantaneous rate of time warping; constraints on the warping can be imposed by assigning the value +inf to the regularization terms. Different choices of the three objective terms yield different time warping functions that trade off signal fit or alignment and properties of the warping function. The optimization problem we formulate is a classical optimal control problem, with initial and terminal constraints, and a state dimension of one. We describe an effective general method that minimizes the objective by discretizing the values of the original and warped time, and using standard dynamic programming to compute the (globally) optimal warping function with the discretized values. Iterated refinement of this scheme yields a high accuracy warping function in just a few iterations. Our method is implemented as an open source Python package GDTW.

In recent years, impressive progress has been made in the design of implicit probabilistic models via Generative Adversarial Networks (GAN) and its extension, the Conditional GAN (CGAN). Excellent solutions have been demonstrated mostly in image processing applications which involve large, continuous output spaces. There is almost no application of these powerful tools to problems having small dimensional output spaces. Regression problems involving the inductive learning of a map, $y=f(x,z)$, $z$ denoting noise, $f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$, with $m$ small (e.g., $m=1$ or just a few) is one good case in point. The standard approach to solve regression problems is to probabilistically model the output $y$ as the sum of a mean function $m(x)$ and a noise term $z$; it is also usual to take the noise to be a Gaussian. These are done for convenience sake so that the likelihood of observed data is expressible in closed form. In the real world, on the other hand, stochasticity of the output is usually caused by missing or noisy input variables. Such a real world situation is best represented using an implicit model in which an extra noise vector, $z$ is included with $x$ as input. CGAN is naturally suited to design such implicit models. This paper makes the first step in this direction. Through several artificial and real world datasets, we demonstrate CGAN to be an effective approach for solving regression problems. We compare against Gaussian Processes and show that CGAN has excellent output likelihood properties and possesses the ability to model complex noise forms in a better way.

Connectivity between different brain regions is one of the most important properties for classification of brain signals including electroencephalography (EEG). However, how to define the connectivity structure for a given task is still an open problem, because there is no ground truth about how the connectivity structure should be in order to maximize the performance. In this paper, we propose an end-to-end neural network model for EEG classification, which can extract an appropriate multi-layer graph structure and signal features directly from a set of raw EEG signals and perform classification. Experimental results demonstrate that our method yields improved performance in comparison to the existing approaches where manually defined connectivity structures and signal features are used. Furthermore, we show that the graph structure extraction process is reliable in terms of consistency, and the learned graph structures make much sense in the neuroscientific viewpoint.

Data-driven approaches which aim to identify and predict player engagement are becoming increasingly popular in games industry contexts. This is due to the growing practice of tracking and storing large volumes of in-game telemetries coupled with a desire to tailor the gaming experience to the end-user's needs. These approaches are particularly useful not just for companies adopting Game-as-a-Service (GaaS) models (e.g. for re-engagement strategies) but also for those working under persistent content-delivery regimes (e.g. for better audience targeting). A major challenge for the latter is to build engagement models of the user which are data-efficient, holistic and can generalize across multiple game titles and genres with minimal adjustments. This work leverages a theoretical framework rooted in engagement and behavioural science research for building a model able to estimate engagement-related behaviours employing only a minimal set of game-agnostic metrics. Through a series of experiments we show how, by modelling early user-game interactions, this approach can make joint estimates of long-term survival time and churn probability across several single-player games in a range of genres. The model proposed is very suitable for industry applications since it relies on a minimal set of metrics and observations, scales well with the number of users and is explicitly designed to work across a diverse range of titles.

Existing deep neural networks (DNNs), say for image classification, have been shown to be vulnerable to adversarial images that can cause a DNN misclassification, without any perceptible change to an image. In this work, we propose "shock-absorbing" robust features such as binarization (e.g., rounding) and group extraction (e.g., color or shape) to augment the classification pipeline, resulting in more robust classifiers. Experimentally, we show that augmenting ML models with these techniques leads to improved overall robustness on adversarial inputs as well as significant improvements in training time. On the MNIST dataset, we achieved 14x speedup in training time to obtain 90% adversarial accuracy compared to the state-of-the-art adversarial training method of Madry et al. [12], as well as retained higher adversarial accuracy over a broader range of attacks. We also find robustness improvements on traffic sign classification using robust feature augmentation. Finally, we give theoretical insights for why one can expect robust feature augmentation to reduce adversarial input space.

We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models for large data, in which the access to the data is restricted in some way. Our main result is that if the regularizer's effect does not become negligible as the norm of the hypothesis scales, and as the data scales, then a uniform sample of modest size is with high probability a coreset. In the case that the loss function is either logistic regression or soft-margin support vector machines, and the regularizer is one of the common recommended choices, this result implies that a uniform sample of size $O(d \sqrt{n})$ is with high probability a coreset of $n$ points in $\Re^d$. We contrast this upper bound with two lower bounds. The first lower bound shows that our analysis of uniform sampling is tight; that is, a smaller uniform sample will likely not be a core set. The second lower bound shows that in some sense uniform sampling is close to optimal, as significantly smaller core sets do not generally exist.