Mixtures of experts have become an indispensable tool for flexible modelling in a supervised learning context, and sparse Gaussian processes (GP) have shown promise as a leading candidate for the experts in such models. In the present article, we propose to design the gating network for selecting the experts from such mixtures of sparse GPs using a deep neural network (DNN). This combination provides a flexible, robust, and efficient model which is able to significantly outperform competing models. We furthermore consider efficient approaches to computing maximum a posteriori (MAP) estimators of these models by iteratively maximizing the distribution of experts given allocations and allocations given experts. We also show that a recently introduced method called Cluster-Classify- Regress (CCR) is capable of providing a good approximation of the optimal solution extremely quickly. This approximation can then be further refined with the iterative algorithm.

Time series with long-term structure arise in a variety of contexts and capturing this temporal structure is a critical challenge in time series analysis for both inference and forecasting settings. Traditionally, state space models have been successful in providing uncertainty estimates of trajectories in the latent space. More recently, deep learning, attention-based approaches have achieved state of the art performance for sequence modeling, though often require large amounts of data and parameters to do so. We propose Stanza, a nonlinear, non-stationary state space model as an intermediate approach to fill the gap between traditional models and modern deep learning approaches for complex time series. Stanza strikes a balance between competitive forecasting accuracy and probabilistic, interpretable inference for highly structured time series. In particular, Stanza achieves forecasting accuracy competitive with deep LSTMs on real-world datasets, especially for multi-step ahead forecasting.

In this work we aimed at comparing our findings in depression detection task with methodologies applied in present literature. Previously we showed that when electrophysiological signal (in this case electroencephalogram, EEG) is characterized by nonlinear measures, any of seven most popular classifiers yields high accuracy on the task. Following every step we done in this process we compare it with other researchers' practice and comment on other findings mainly from analysis of electrical signals or nonlinear analysis showing what would be optimal for further research. We focused on discussing various mistakes and differences that could potentially lead to unwarranted optimism and other misinterpretation of results. In Conclusion we summarize recommendation for future research in order to be applicable in clinical practice. Introduction Current clinical psychiatry is lacking objective biochemical or electrophysiological tests used for diagnosis unlike other medical disciplines. To diagnose depression, clinician will typically rely on the self-report from the patient and his experience in applying DSM manual, which is standardized list of symptoms to be checked in every case (in order to be qualified as a certain disorder). It is perfectly possible that two persons diagnosed with the same disorder have not overlapping symptoms, and that one person can have two distinct diagnosis. If someone has more than three episodes of depression, that is considered to be recurrent depression (after every episode the probability of the next one is doubling). This is particularly heard to treat and manage therapy which is ongoing through person's whole life. Apart from obsolete diagnostic, all antidepressants have serious side-effects, the waiting lists are very long (in Nederland they are between 6 and 9 months long) and the therapy can last for years or even decades. It is reported than only 11 - 30% of patients are improving in the first year of therapy (Rush et al., 2008).

Thompson sampling has become a ubiquitous approach to online decision problems with bandit feedback. The key algorithmic task for Thompson sampling is drawing a sample from the posterior of the optimal action. We propose an alternative arm selection rule we dub TS-UCB, that requires negligible additional computational effort but provides significant performance improvements relative to Thompson sampling. At each step, TS-UCB computes a score for each arm using two ingredients: posterior sample(s) and upper confidence bounds. TS-UCB can be used in any setting where these two quantities are available, and it is flexible in the number of posterior samples it takes as input. This proves particularly valuable in heuristics for deep contextual bandits: we show that TS-UCB achieves materially lower regret on all problem instances in a deep bandit suite proposed in Riquelme et al. (2018). Finally, from a theoretical perspective, we establish optimal regret guarantees for TS-UCB for both the K-armed and linear bandit models.

Deep candidate generation (DCG) that narrows down the collection of relevant items from billions to hundreds via representation learning is essential to large-scale recommender systems. Standard approaches approximate maximum likelihood estimation (MLE) through sampling for better scalability and address the problem of DCG in a way similar to language modeling. However, live recommender systems face severe unfairness of exposure with a vocabulary several orders of magnitude larger than that of natural language, implying that (1) MLE will preserve and even exacerbate the exposure bias in the long run in order to faithfully fit the observed samples, and (2) suboptimal sampling and inadequate use of item features can lead to inferior representations for the unfairly ignored items. In this paper, we introduce CLRec, a Contrastive Learning paradigm that has been successfully deployed in a real-world massive recommender system, to alleviate exposure bias in DCG. We theoretically prove that a popular choice of contrastive loss is equivalently reducing the exposure bias via inverse propensity scoring, which provides a new perspective on the effectiveness of contrastive learning. We further employ a fixed-size queue to store the items' representations computed in previously processed batches, and use the queue to serve as an effective sampler of negative examples. This queue-based design provides great efficiency in incorporating rich features of the thousand negative items per batch thanks to computation reuse. Extensive offline analyses and four-month online A/B tests in Mobile Taobao demonstrate substantial improvement, including a dramatic reduction in the Matthew effect.

Generative Adversarial Network (GAN) can be viewed as an implicit estimator of a data distribution, and this perspective motivates using the adversarial concept in the true input parameter estimation of black-box generators. While previous works on likelihood-free inference introduces an implicit proposal distribution on the generator input, this paper analyzes theoretic limitations of the proposal distribution approach. On top of that, we introduce a new algorithm, Adversarial Likelihood-Free Inference (ALFI), to mitigate the analyzed limitations, so ALFI is able to find the posterior distribution on the input parameter for black-box generative models. We experimented ALFI with diverse simulation models as well as pre-trained statistical models, and we identified that ALFI achieves the best parameter estimation accuracy with a limited simulation budget.

Evaluating treatment effect heterogeneity widely informs treatment decision making. At the moment, much emphasis is placed on the estimation of the conditional average treatment effect via flexible machine learning algorithms. While these methods enjoy some theoretical appeal in terms of consistency and convergence rates, they generally perform poorly in terms of uncertainty quantification. This is troubling since assessing risk is crucial for reliable decision-making in sensitive and uncertain environments. In this work, we propose a conformal inference-based approach that can produce reliable interval estimates for counterfactuals and individual treatment effects under the potential outcome framework. For completely randomized or stratified randomized experiments with perfect compliance, the intervals have guaranteed average coverage in finite samples regardless of the unknown data generating mechanism. For randomized experiments with ignorable compliance and general observational studies obeying the strong ignorability assumption, the intervals satisfy a doubly robust property which states the following: the average coverage is approximately controlled if either the propensity score or the conditional quantiles of potential outcomes can be estimated accurately. Numerical studies on both synthetic and real datasets empirically demonstrate that existing methods suffer from a significant coverage deficit even in simple models. In contrast, our methods achieve the desired coverage with reasonably short intervals.

Learning from demonstrations (LfD) improves the exploration efficiency of a learning agent by incorporating demonstrations from experts. However, demonstration data can often come from multiple experts with conflicting goals, making it difficult to incorporate safely and effectively in online settings. We address this problem in the static and dynamic optimization settings by modelling the uncertainty in source and target task functions using normal-inverse-gamma priors, whose corresponding posteriors are, respectively, learned from demonstrations and target data using Bayesian neural networks with shared features. We use this learned belief to derive a quadratic programming problem whose solution yields a probability distribution over the expert models. Finally, we propose Bayesian Experience Reuse (BERS) to sample demonstrations in accordance with this distribution and reuse them directly in new tasks. We demonstrate the effectiveness of this approach for static optimization of smooth functions, and transfer learning in a high-dimensional supply chain problem with cost uncertainty.

We consider shared workspace scenarios with humans and robots acting to achieve independent goals, termed as parallel play. We model these as general-sum games and construct a framework that utilizes the Nash equilibrium solution concept to consider the interactive effect of both agents while planning. We find multiple Pareto-optimal equilibria in these tasks. We hypothesize that people act by choosing an equilibrium based on social norms and their personalities. To enable coordination, we infer the equilibrium online using a probabilistic model that includes these two factors and use it to select the robot's action. We apply our approach to a close-proximity pick-and-place task involving a robot and a simulated human with three potential behaviors - defensive, selfish, and norm-following. We showed that using a Bayesian approach to infer the equilibrium enables the robot to complete the task with less than half the number of collisions while also reducing the task execution time as compared to the best baseline. We also performed a study with human participants interacting either with other humans or with different robot agents and observed that our proposed approach performs similar to human-human parallel play interactions. The code is available at https://github.com/shray/bayes-nash

The use of machine learning (ML) in high-stakes societal decisions has encouraged the consideration of fairness throughout the ML lifecycle. Although data integration is one of the primary steps to generate high quality training data, most of the fairness literature ignores this stage. In this work, we consider fairness in the integration component of data management, aiming to identify features that improve prediction without adding any bias to the dataset. We work under the causal interventional fairness paradigm. Without requiring the underlying structural causal model a priori, we propose an approach to identify a sub-collection of features that ensure the fairness of the dataset by performing conditional independence tests between different subsets of features. We use group testing to improve the complexity of the approach. We theoretically prove the correctness of the proposed algorithm to identify features that ensure interventional fairness and show that sub-linear conditional independence tests are sufficient to identify these variables. A detailed empirical evaluation is performed on real-world datasets to demonstrate the efficacy and efficiency of our technique.