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Offline policy evaluation (OPE) is considered a fundamental and challenging problem in reinforcement learning (RL). This paper focuses on the value estimation of a target policy based on pre-collected data generated from a possibly different policy, under the framework of infinite-horizon Markov decision processes. Motivated by the recently developed marginal importance sampling method in RL and the covariate balancing idea in causal inference, we propose a novel estimator with approximately projected state-action balancing weights for the policy value estimation. We obtain the convergence rate of these weights, and show that the proposed value estimator is semi-parametric efficient under technical conditions. In terms of asymptotics, our results scale with both the number of trajectories and the number of decision points at each trajectory. As such, consistency can still be achieved with a limited number of subjects when the number of decision points diverges. In addition, we make a first attempt towards characterizing the difficulty of OPE problems, which may be of independent interest. Numerical experiments demonstrate the promising performance of our proposed estimator.

In this paper, we proposed a multi-objective approach for the EEG Inverse Problem. This formulation does not need unknown parameters that involve empirical procedures. Due to the combinatorial characteristics of the problem, this alternative included evolutionary strategies to resolve it. The result is a Multi-objective Evolutionary Algorithm based on Anatomical Restrictions (MOEAAR) to estimate distributed solutions. The comparative tests were between this approach and 3 classic methods of regularization: LASSO, Ridge-L and ENET-L. In the experimental phase, regression models were selected to obtain sparse and distributed solutions. The analysis involved simulated data with different signal-to-noise ratio (SNR). The indicators for quality control were Localization Error, Spatial Resolution and Visibility. The MOEAAR evidenced better stability than the classic methods in the reconstruction and localization of the maximum activation. The norm L0 was used to estimate sparse solutions with the evolutionary approach and its results were relevant.

Pervasive cross-section dependence is increasingly recognized as an appropriate characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure, early work established convergence of the principal component estimates of the factors and loadings to a rotation matrix. This paper shows that the estimates are still consistent and asymptotically normal for a broad range of weaker factor loadings, albeit at slower rates and under additional assumptions on the sample size. Standard inference procedures can be used except in the case of extremely weak loadings which has encouraging implications for empirical work. The simplified proofs are of independent interest.

It has become an increasingly common practice for scientists in modern science and engineering to collect samples of multiple network data in which a network serves as a basic data object. The increasing prevalence of multiple network data calls for developments of models and theory that can deal with inference problems for populations of networks. In this work, we propose a general procedure for hypothesis testing of networks and in particular, for differentiating distributions of two samples of networks. We consider a very general framework which allows us to perform tests on large and sparse networks. Our contribution is two-fold: (1) We propose a test statistics based on the singular value of a generalized Wigner matrix. The asymptotic null distribution of the statistics is shown to follow the Tracy--Widom distribution as the number of nodes tends to infinity. The test also yields asymptotic power guarantee with the power tending to one under the alternative; (2) The test procedure is adapted for change-point detection in dynamic networks which is proven to be consistent in detecting the change-points. In addition to theoretical guarantees, another appealing feature of this adapted procedure is that it provides a principled and simple method for selecting the threshold that is also allowed to vary with time. Extensive simulation studies and real data analyses demonstrate the superior performance of our procedure with competitors.

We consider the use of Gaussian process (GP) priors for solving inverse problems in a Bayesian framework. As is well known, the computational complexity of GPs scales cubically in the number of datapoints. We here show that in the context of inverse problems involving integral operators, one faces additional difficulties that hinder inversion on large grids. Furthermore, in that context, covariance matrices can become too large to be stored. By leveraging results about sequential disintegrations of Gaussian measures, we are able to introduce an implicit representation of posterior covariance matrices that reduces the memory footprint by only storing low rank intermediate matrices, while allowing individual elements to be accessed on-the-fly without needing to build full posterior covariance matrices. Moreover, it allows for fast sequential inclusion of new observations. These features are crucial when considering sequential experimental design tasks. We demonstrate our approach by computing sequential data collection plans for excursion set recovery for a gravimetric inverse problem, where the goal is to provide fine resolution estimates of high density regions inside the Stromboli volcano, Italy. Sequential data collection plans are computed by extending the weighted integrated variance reduction (wIVR) criterion to inverse problems. Our results show that this criterion is able to significantly reduce the uncertainty on the excursion volume, reaching close to minimal levels of residual uncertainty. Overall, our techniques allow the advantages of probabilistic models to be brought to bear on large-scale inverse problems arising in the natural sciences.

This paper studies the rates of convergence for learning distributions implicitly with the adversarial framework and Generative Adversarial Networks (GANs), which subsume Wasserstein, Sobolev, MMD GAN, and Generalized/Simulated Method of Moments (GMM/SMM) as special cases. We study a wide range of parametric and nonparametric target distributions under a host of objective evaluation metrics. We investigate how to obtain valid statistical guarantees for GANs through the lens of regularization. On the nonparametric end, we derive the optimal minimax rates for distribution estimation under the adversarial framework. On the parametric end, we establish a theory for general neural network classes (including deep leaky ReLU networks) that characterizes the interplay on the choice of generator and discriminator pair. We discover and isolate a new notion of regularization, called the generator-discriminator-pair regularization, that sheds light on the advantage of GANs compared to classical parametric and nonparametric approaches for explicit distribution estimation. We develop novel oracle inequalities as the main technical tools for analyzing GANs, which are of independent interest.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.

Few-shot Learning aims to learn classifiers for new classes with only a few training examples per class. Existing meta-learning or metric-learning based few-shot learning approaches are limited in handling diverse domains with various number of labels. The meta-learning approaches train a meta learner to predict weights of homogeneous-structured task-specific networks, requiring a uniform number of classes across tasks. The metric-learning approaches learn one task-invariant metric for all the tasks, and they fail if the tasks diverge. We propose to deal with these limitations with meta metric learning. Our meta metric learning approach consists of task-specific learners, that exploit metric learning to handle flexible labels, and a meta learner, that discovers good parameters and gradient decent to specify the metrics in task-specific learners. Thus the proposed model is able to handle unbalanced classes as well as to generate task-specific metrics. We test our approach in the `$k$-shot $N$-way' few-shot learning setting used in previous work and new realistic few-shot setting with diverse multi-domain tasks and flexible label numbers. Experiments show that our approach attains superior performances in both settings.

Matter evolved under influence of gravity from minuscule density fluctuations. Non-perturbative structure formed hierarchically over all scales, and developed non-Gaussian features in the Universe, known as the Cosmic Web. To fully understand the structure formation of the Universe is one of the holy grails of modern astrophysics. Astrophysicists survey large volumes of the Universe and employ a large ensemble of computer simulations to compare with the observed data in order to extract the full information of our own Universe. However, to evolve trillions of galaxies over billions of years even with the simplest physics is a daunting task. We build a deep neural network, the Deep Density Displacement Model (hereafter D$^3$M), to predict the non-linear structure formation of the Universe from simple linear perturbation theory. Our extensive analysis, demonstrates that D$^3$M outperforms the second order perturbation theory (hereafter 2LPT), the commonly used fast approximate simulation method, in point-wise comparison, 2-point correlation, and 3-point correlation. We also show that D$^3$M is able to accurately extrapolate far beyond its training data, and predict structure formation for significantly different cosmological parameters. Our study proves, for the first time, that deep learning is a practical and accurate alternative to approximate simulations of the gravitational structure formation of the Universe.

Attributes, such as metadata and profile, carry useful information which in principle can help improve accuracy in recommender systems. However, existing approaches have difficulty in fully leveraging attribute information due to practical challenges such as heterogeneity and sparseness. These approaches also fail to combine recurrent neural networks which have recently shown effectiveness in item recommendations in applications such as video and music browsing. To overcome the challenges and to harvest the advantages of sequence models, we present a novel approach, Heterogeneous Attribute Recurrent Neural Networks (HA-RNN), which incorporates heterogeneous attributes and captures sequential dependencies in \textit{both} items and attributes. HA-RNN extends recurrent neural networks with 1) a hierarchical attribute combination input layer and 2) an output attribute embedding layer. We conduct extensive experiments on two large-scale datasets. The new approach show significant improvements over the state-of-the-art models. Our ablation experiments demonstrate the effectiveness of the two components to address heterogeneous attribute challenges including variable lengths and attribute sparseness. We further investigate why sequence modeling works well by conducting exploratory studies and show sequence models are more effective when data scale increases.