We address uncertainty quantification for Gaussian processes (GPs) under misspecified priors, with an eye towards Bayesian Optimization (BO). GPs are widely used in BO because they easily enable exploration based on posterior uncertainty bands. However, this convenience comes at the cost of robustness: a typical function encountered in practice is unlikely to have been drawn from the data scientist's prior, in which case uncertainty estimates can be misleading, and the resulting exploration can be suboptimal. This brittle behavior is convincingly demonstrated in simple simulations. We present a frequentist approach to GP/BO uncertainty quantification. We utilize the GP framework as a working model, but do not assume correctness of the prior. We instead construct a confidence sequence (CS) for the unknown function using martingale techniques. There is a necessary cost to achieving robustness: if the prior was correct, posterior GP bands are narrower than our CS. Nevertheless, when the prior is wrong, our CS is statistically valid and empirically outperforms standard GP methods, in terms of both coverage and utility for BO. Additionally, we demonstrate that powered likelihoods provide robustness against model misspecification.

Targeted Learning is a subfield of statistics that unifies advances in causal inference, machine learning and statistical theory to help answer scientifically impactful questions with statistical confidence. Targeted Learning is driven by complex problems in data science and has been implemented in a diversity of real-world scenarios: observational studies with missing treatments and outcomes, personalized interventions, longitudinal settings with time-varying treatment regimes, survival analysis, adaptive randomized trials, mediation analysis, and networks of connected subjects. In contrast to the (mis)application of restrictive modeling strategies that dominate the current practice of statistics, Targeted Learning establishes a principled standard for statistical estimation and inference (i.e., confidence intervals and p-values). This multiply robust approach is accompanied by a guiding roadmap and a burgeoning software ecosystem, both of which provide guidance on the construction of estimators optimized to best answer the motivating question. The roadmap of Targeted Learning emphasizes tailoring statistical procedures so as to minimize their assumptions, carefully grounding them only in the scientific knowledge available. The end result is a framework that honestly reflects the uncertainty in both the background knowledge and the available data in order to draw reliable conclusions from statistical analyses -- ultimately enhancing the reproducibility and rigor of scientific findings.

A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of parameters for the SM kernel typically induces an over-fitting, particularly when a gradient-based optimization is used. Also, a longer training time is required. To improve the training, we propose an approximate Bayesian inference for the SM kernel. Specifically, we employ the variational distribution of the spectral points to approximate SM kernel with a random Fourier feature. We optimize the variational parameters by applying a sampling-based variational inference to the derived evidence lower bound (ELBO) estimator constructed from the approximate kernel. To improve the inference, we further propose two additional strategies: (1) a sampling strategy of spectral points to estimate the ELBO estimator reliably and thus its associated gradient, and (2) an approximate natural gradient to accelerate the convergence of the parameters. The proposed inference combined with two strategies accelerates the convergence of the parameters and leads to better optimal parameters.

We present a new approach for sampling conditional measures that enables uncertainty quantification in supervised learning tasks. We construct a mapping that transforms a reference measure to the probability measure of the output conditioned on new inputs. The mapping is trained via a modification of generative adversarial networks (GANs), called monotone GANs, that imposes monotonicity constraints and a block triangular structure. We present theoretical results, in an idealized setting, that support our proposed method as well as numerical experiments demonstrating the ability of our method to sample the correct conditional measures in applications ranging from inverse problems to image in-painting.

Local structure such as context-specific independence (CSI) has received much attention in the probabilistic graphical model (PGM) literature, as it facilitates the modeling of large complex systems, as well as for reasoning with them. In this paper, we provide a new perspective on how to learn CSIs from data. We propose to first learn a functional and parameterized representation of a conditional probability table (CPT), such as a neural network. Next, we quantize this continuous function, into an arithmetic circuit representation that facilitates efficient inference. In the first step, we can leverage the many powerful tools that have been developed in the machine learning literature. In the second step, we exploit more recently-developed analytic tools from explainable AI, for the purposes of learning CSIs. Finally, we contrast our approach, empirically and conceptually, with more traditional variable-splitting approaches, that search for CSIs more explicitly.

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.