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We consider the conditional treatment effect for competing risks data in observational studies. While it is described as a constant difference between the hazard functions given the covariates, we do not assume specific functional forms for the covariates. We derive the efficient score for the treatment effect using modern semiparametric theory, as well as two doubly robust scores with respect to 1) the assumed propensity score for treatment and the censoring model, and 2) the outcome models for the competing risks. An important asymptotic result regarding the estimators is rate double robustness, in addition to the classical model double robustness. Rate double robustness enables the use of machine learning and nonparametric methods in order to estimate the nuisance parameters, while preserving the root-$n$ asymptotic normality of the estimators for inferential purposes. We study the performance of the estimators using simulation. The estimators are applied to the data from a cohort of Japanese men in Hawaii followed since 1960s in order to study the effect of mid-life drinking behavior on late life cognitive outcomes.

We propose nonparametric estimators for the second-order central moments of spherical random fields within a functional data context. We consider a measurement framework where each field among an identically distributed collection of spherical random fields is sampled at a few random directions, possibly subject to measurement error. The collection of fields could be i.i.d. or serially dependent. Though similar setups have already been explored for random functions defined on the unit interval, the nonparametric estimators proposed in the literature often rely on local polynomials, which do not readily extend to the (product) spherical setting. We therefore formulate our estimation procedure as a variational problem involving a generalized Tikhonov regularization term. The latter favours smooth covariance/autocovariance functions, where the smoothness is specified by means of suitable Sobolev-like pseudo-differential operators. Using the machinery of reproducing kernel Hilbert spaces, we establish representer theorems that fully characterizing the form of our estimators. We determine their uniform rates of convergence as the number of fields diverges, both for the dense (increasing number of spatial samples) and sparse (bounded number of spatial samples) regimes. We moreover validate and demonstrate the practical feasibility of our estimation procedure in a simulation setting, assuming a fixed number of samples per field. Our numerical estimation procedure leverages the sparsity and second-order Kronecker structure of our setup to reduce the computational and memory requirements by approximately three orders of magnitude compared to a naive implementation would require.

The presence of unobserved node specific heterogeneity in Exponential Random Graph Models (ERGM) is a general concern, both with respect to model validity as well as estimation instability. We therefore extend the ERGM by including node specific random effects that account for unobserved heterogeneity in the network. This leads to a mixed model with parametric as well as random coefficients, labelled as mixed ERGM. Estimation is carried out by combining approximate penalized pseudolikelihood estimation for the random effects with maximum likelihood estimation for the remaining parameters in the model. This approach provides a stable algorithm, which allows to fit nodal heterogeneity effects even for large scale networks. We also propose model selection based on the AIC to check for node specific heterogeneity.

When the sizes of the state and action spaces are large, solving MDPs can be computationally prohibitive even if the probability transition matrix is known. So in practice, a number of techniques are used to approximately solve the dynamic programming problem, including lookahead, approximate policy evaluation using an m-step return, and function approximation. In a recent paper, (Efroni et al. 2019) studied the impact of lookahead on the convergence rate of approximate dynamic programming. In this paper, we show that these convergence results change dramatically when function approximation is used in conjunction with lookout and approximate policy evaluation using an m-step return. Specifically, we show that when linear function approximation is used to represent the value function, a certain minimum amount of lookahead and multi-step return is needed for the algorithm to even converge. And when this condition is met, we characterize the performance of policies obtained using such approximate policy iteration. Our results are presented for two different procedures to compute the function approximation: linear least-squares regression and gradient descent.

We propose a new adaptive hypothesis test for polyhedral cone (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test statistic is based on a modified leave-one-out sample analog of a quadratic distance between the restricted and unrestricted sieve NPIV estimators. We provide computationally simple, data-driven choices of sieve tuning parameters and adjusted chi-squared critical values. Our test adapts to the unknown smoothness of alternative functions in the presence of unknown degree of endogeneity and unknown strength of the instruments. It attains the adaptive minimax rate of testing in $L^2$. That is, the sum of its type I error uniformly over the composite null and its type II error uniformly over nonparametric alternative models cannot be improved by any other hypothesis test for NPIV models of unknown regularities. Data-driven confidence sets in $L^2$ are obtained by inverting the adaptive test. Simulations confirm that our adaptive test controls size and its finite-sample power greatly exceeds existing non-adaptive tests for monotonicity and parametric restrictions in NPIV models. Empirical applications to test for shape restrictions of differentiated products demand and of Engel curves are presented.

We introduce a nonparametric nonlinear VAR prewhitened long-run variance (LRV) estimator for the construction of standard errors robust to autocorrelation and heteroskedasticity that can be used for hypothesis testing in a variety of contexts including the linear regression model. Existing methods either are theoretically valid only under stationarity and have poor finite-sample properties under nonstationarity (i.e., fixed-b methods), or are theoretically valid under the null hypothesis but lead to tests that are not consistent under nonstationary alternative hypothesis (i.e., both fixed-b and traditional HAC estimators). The proposed estimator accounts explicitly for nonstationarity, unlike previous prewhitened procedures which are known to be unreliable, and leads to tests with accurate null rejection rates and good monotonic power. We also establish MSE bounds for LRV estimation that are sharper than previously established and use them to determine the data-dependent bandwidths.

This paper addresses the problem of viewpoint estimation of an object in a given image. It presents five key insights that should be taken into consideration when designing a CNN that solves the problem. Based on these insights, the paper proposes a network in which (i) The architecture jointly solves detection, classification, and viewpoint estimation. (ii) New types of data are added and trained on. (iii) A novel loss function, which takes into account both the geometry of the problem and the new types of data, is propose. Our network improves the state-of-the-art results for this problem by 9.8%.

We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.

Detecting objects and estimating their pose remains as one of the major challenges of the computer vision research community. There exists a compromise between localizing the objects and estimating their viewpoints. The detector ideally needs to be view-invariant, while the pose estimation process should be able to generalize towards the category-level. This work is an exploration of using deep learning models for solving both problems simultaneously. For doing so, we propose three novel deep learning architectures, which are able to perform a joint detection and pose estimation, where we gradually decouple the two tasks. We also investigate whether the pose estimation problem should be solved as a classification or regression problem, being this still an open question in the computer vision community. We detail a comparative analysis of all our solutions and the methods that currently define the state of the art for this problem. We use PASCAL3D+ and ObjectNet3D datasets to present the thorough experimental evaluation and main results. With the proposed models we achieve the state-of-the-art performance in both datasets.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.