Machine learning can help personalized decision support by learning models to predict individual treatment effects (ITE). This work studies the reliability of prediction-based decision-making in a task of deciding which action $a$ to take for a target unit after observing its covariates $\tilde{x}$ and predicted outcomes $\hat{p}(\tilde{y} \mid \tilde{x}, a)$. An example case is personalized medicine and the decision of which treatment to give to a patient. A common problem when learning these models from observational data is imbalance, that is, difference in treated/control covariate distributions, which is known to increase the upper bound of the expected ITE estimation error. We propose to assess the decision-making reliability by estimating the ITE model's Type S error rate, which is the probability of the model inferring the sign of the treatment effect wrong. Furthermore, we use the estimated reliability as a criterion for active learning, in order to collect new (possibly expensive) observations, instead of making a forced choice based on unreliable predictions. We demonstrate the effectiveness of this decision-making aware active learning in two decision-making tasks: in simulated data with binary outcomes and in a medical dataset with synthetic and continuous treatment outcomes.

There is a growing body of work that proposes methods for mitigating bias in machine learning systems. These methods typically rely on access to protected attributes such as race, gender, or age. However, this raises two significant challenges: (1) protected attributes may not be available or it may not be legal to use them, and (2) it is often desirable to simultaneously consider multiple protected attributes, as well as their intersections. In the context of mitigating bias in occupation classification, we propose a method for discouraging correlation between the predicted probability of an individual's true occupation and a word embedding of their name. This method leverages the societal biases that are encoded in word embeddings, eliminating the need for access to protected attributes. Crucially, it only requires access to individuals' names at training time and not at deployment time. We evaluate two variations of our proposed method using a large-scale dataset of online biographies. We find that both variations simultaneously reduce race and gender biases, with almost no reduction in the classifier's overall true positive rate.

Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We solve a Fourier-like generalised harmonic feature representation of the GP prior in the domain of interest, which both constrains the GP and attains a low-rank representation that is used for speeding up inference. The method scales as $\mathcal{O}(nm^2)$ in prediction and $\mathcal{O}(m^3)$ in hyperparameter learning for regression, where $n$ is the number of data points and $m$ the number of features. Furthermore, we make use of the variational approach to allow the method to deal with non-Gaussian likelihoods. The experiments cover both simulated and empirical data in which the boundary conditions allow for inclusion of additional physical information.

Weighted log-rank tests are arguably the most widely used tests by practitioners for the two-sample problem in the context of right-censored data. Many approaches have been considered to make weighted log-rank tests more robust against a broader family of alternatives, among them: considering linear combinations of weighted log-rank tests or taking the maximum between a finite collection of them. In this paper, we propose as test-statistic the supremum of a collection of (potentially infinite) weight-indexed log-rank tests where the index space is the unit ball of a reproducing kernel Hilbert space (RKHS). By using the good properties of the RKHS's we provide an exact and simple evaluation of the test-statistic and establish relationships between previous tests in the literature. Additionally, we show that for a special family of RKHS's, the proposed test is omnibus. We finalise by performing an empirical evaluation of the proposed methodology and show an application to a real data scenario.

Multitask algorithms typically use task similarity information as a bias to speed up and improve the performance of learning processes. Tasks are learned jointly, sharing information across them, in order to construct models more accurate than those learned separately over single tasks. In this contribution, we present the first multitask model, to our knowledge, based on Hopfield Networks (HNs), named HoMTask. We show that by appropriately building a unique HN embedding all tasks, a more robust and effective classification model can be learned. HoMTask is a transductive semi-supervised parametric HN, that minimizes an energy function extended to all nodes and to all tasks under study. We provide theoretical evidence that the optimal parameters automatically estimated by HoMTask make coherent the model itself with the prior knowledge (connection weights and node labels). The convergence properties of HNs are preserved, and the fixed point reached by the network dynamics gives rise to the prediction of unlabeled nodes. The proposed model improves the classification abilities of singletask HNs on a preliminary benchmark comparison, and achieves competitive performance with state-of-the-art semi-supervised graph-based algorithms.

Generalization and reliability of multilingual translation often highly depend on the amount of available parallel data for each language pair of interest. In this paper, we focus on zero-shot generalization---a challenging setup that tests models on translation directions they have not been optimized for at training time. To solve the problem, we (i) reformulate multilingual translation as probabilistic inference, (ii) define the notion of zero-shot consistency and show why standard training often results in models unsuitable for zero-shot tasks, and (iii) introduce a consistent agreement-based training method that encourages the model to produce equivalent translations of parallel sentences in auxiliary languages. We test our multilingual NMT models on multiple public zero-shot translation benchmarks (IWSLT17, UN corpus, Europarl) and show that agreement-based learning often results in 2-3 BLEU zero-shot improvement over strong baselines without any loss in performance on supervised translation directions.

This study investigates the effects of Markov Chain Monte Carlo (MCMC) sampling in unsupervised Maximum Likelihood (ML) learning. Our attention is restricted to the family of unnormalized probability densities for which the negative log density (or energy function) is a ConvNet. In general, we find that many of the techniques used to stabilize training in previous studies can have the opposite effect. Stable ML learning with a ConvNet potential can be achieved with only a few hyper-parameters and no regularization. Using this minimal framework, we identify a variety of ML learning outcomes that depend on the implementation of MCMC sampling. On one hand, we show that it is easy to train an energy-based model which can sample realistic images with short-run Langevin. ML can be effective and stable even when MCMC samples have much higher energy than true steady-state samples throughout training. Based on this insight, we introduce an ML method with purely noise-initialized MCMC, high-quality short-run synthesis, and the same budget as ML with informative MCMC initialization such as CD or PCD. Unlike previous models, our model can obtain realistic high-diversity samples from a noise signal after training with no auxiliary networks. On the other hand, ConvNet potentials learned with highly non-convergent MCMC do not have a valid steady-state and cannot be considered approximate unnormalized densities of the training data because long-run MCMC samples differ greatly from observed images. We show that it is much harder to train a ConvNet potential to learn a steady-state over realistic images. To our knowledge, long-run MCMC samples of all previous models lose the realism of short-run samples. With correct tuning of Langevin noise, we train the first ConvNet potentials for which long-run and steady-state MCMC samples are realistic images.

We study the approximation efficiency of function compositions in nonlinear approximation, especially the case when compositions are implemented using multi-layer feed-forward neural networks (FNNs) with ReLU activation functions. The central question of interest is what are the advantages of function compositions in generating dictionaries and what is the optimal implementation of function compositions via ReLU FNNs, especially in modern computing architecture. This question is answered by studying the $N$-term approximation rate, which is the decrease in error versus the number of computational nodes (neurons) in the approximant, together with parallel efficiency for the first time. First, for an arbitrary function $f$ on $[0,1]$, regardless of its smoothness and even the continuity, if $f$ can be approximated via nonlinear approximation using one-hidden-layer ReLU FNNs with an approximation rate $O(N^{-\eta})$, we quantitatively show that dictionaries with function compositions via deep ReLU FNNs can improve the approximation rate to $O(N^{-2\eta})$. Second, for H{\"o}lder continuous functions of order $\alpha$ with a uniform Lipchitz constant $\omega$ on a $d$-dimensional cube, we show that the $N$-term approximation via ReLU FNNs with two or three function compositions can achieve an approximation rate $O( N^{-2\alpha/d})$. The approximation rate can be improved to $O(L^{-2\alpha/d})$ by composing $L$ times, if $N$ is fixed and sufficiently large; but further compositions cannot achieve the approximation rate $O(N^{-\alpha L/d})$. Finally, considering the computational efficiency per training iteration in parallel computing, FNNs with $O(1)$ hidden layers are an optimal choice for approximating H{\"o}lder continuous functions if computing resources are enough.

Liquid democracy is a collective decision making paradigm which lies between direct and representative democracy. One of its main features is that voters can delegate their votes in a transitive manner such that: A delegates to B and B delegates to C leads to A indirectly delegates to C. These delegations can be effectively empowered by implementing liquid democracy in a social network, so that voters can delegate their votes to any of their neighbors in the network. However, it is uncertain that such a delegation process will lead to a stable state where all voters are satisfied with the people representing them. We study the stability (w.r.t. voters preferences) of the delegation process in liquid democracy and model it as a game in which the players are the voters and the strategies are their possible delegations. We answer several questions on the equilibria of this process in any social network or in social networks that correspond to restricted types of graphs. We show that a Nash-equilibrium may not exist, and that it is even NP-complete to decide whether one exists or not. This holds even if the social network is a complete graph or a bounded degree graph. We further show that this existence problem is W[1]-hard w.r.t. the treewidth of the social network. Besides these hardness results, we demonstrate that an equilibrium always exists whatever the preferences of the voters iff the social network is a tree. We design a dynamic programming procedure to determine some desirable equilibria (e.g., minimizing the dissatisfaction of the voters) in polynomial time for tree social networks. Lastly, we study the convergence of delegation dynamics. Unfortunately, when an equilibrium exists, we show that a best response dynamics may not converge, even if the social network is a path or a complete graph.

Quantitative Susceptibility Mapping (QSM) reconstruction is a challenging inverse problem driven by ill conditioning of its field-to -susceptibility transformation. State-of-art QSM reconstruction methods either suffer from image artifacts or long computation times, which limits QSM clinical translation efforts. To overcome these limitations, a non-locally encoder-decoder gated convolutional neural network is trained to infer whole brain susceptibility map, using the local field and brain mask as the inputs. The performance of the proposed method is evaluated relative to synthetic data, a publicly available challenge dataset, and clinical datasets. The proposed approach can outperform existing methods on quantitative metrics and visual assessment of image sharpness and streaking artifacts. The estimated susceptibility maps can preserve conspicuity of fine features and suppress streaking artifacts. The demonstrated methods have potential value in advancing QSM clinical research and aiding in the translation of QSM to clinical operations.