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Kobe Bryant was already immortal. Bryant and fellow NBA greats Tim Duncan and Kevin Garnett headlined a nine-person group announced Saturday as this year’s class of enshrinees into the Naismith Memorial Basketball Hall of Fame. Two-time NBA champion coach Rudy Tomjanovich finally got his call, as did longtime Baylor women’s coach Kim Mulkey, 1,000-game winner Barbara Stevens of Bentley and three-time Final Four coach Eddie Sutton.

Arizona's Aari McDonald and Pac-12 Networks' Ashley Adamson discuss the guard's decision to return for her senior season in Tucson and how she now has the opportunity to be the face of the league. McDonald, the Pac-12 Defensive Player of the Year, was one of the nation's top scorers in 2019-20, averaging 20.6 points per game.

UCLA guard Japreece Dean is primed to shine at the next level as she heads to the WNBA Draft in April. The do-it-all point-woman was an All-Pac-12 honoree last season, and one of only seven D-1 hoopers with at least 13 points and 5.5 assists per game.

The Tennessee Lady Vols have added forward-center Keyen Green as a graduate transfer from Liberty. Coach Kellie Harper announced Wednesday that Green has signed a scholarship for the upcoming season. The 6-foot-1 Green spent the past four seasons at Liberty and graduated in May 2019.

LEXINGTON, Ky. (AP) -- Sophomore guards Jazmine Massengill and Robyn Benton transferred to Kentucky from Southeastern Conference rivals Wednesday.

See some of Sabrina Ionescu's remarkable accomplishments at Oregon set to the Star Wars opening crawl.

The Pac-12 Student-Athlete Advisory Committee voted to award the Oregon State women’s basketball team with the Pac-12 Sportsmanship Award for the 2019-20 season, honoring their character and sportsmanship before a rivalry game against Oregon in Jan. 2020 -- the day Kobe Bryant, his daughter, Gigi, and seven others passed away in a helicopter crash in Southern California. In the above video, Aleah Goodman and Madison Washington share how the teams came together as one in a circle of prayer before the game.

Pac-12 student-athletes give shout-outs to their moms ahead of Mother's Day on May 10th, 2020 including UCLA's Michaela Onyenwere, Oregon's Sabrina Ionescu and Satou Sabally, Arizona's Aari McDonald, Cate Reese, and Lacie Hull, Stanford's Kiana Williams, USC's Endyia Rogers, and Aliyah Jeune, and Utah's Brynna Maxwell.

Heiko Werner, Hajo Holzmann, Pierre Vandekerkhove.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1816--1871.

Abstract:
We investigate a flexible two-component semiparametric mixture of regressions model, in which one of the conditional component distributions of the response given the covariate is unknown but assumed symmetric about a location parameter, while the other is specified up to a scale parameter. The location and scale parameters together with the proportion are allowed to depend nonparametrically on covariates. After settling identifiability, we provide local M-estimators for these parameters which converge in the sup-norm at the optimal rates over Hölder-smoothness classes. We also introduce an adaptive version of the estimators based on the Lepski-method. Sup-norm bounds show that the local M-estimator properly estimates the functions globally, and are the first step in the construction of useful inferential tools such as confidence bands. In our analysis we develop general results about rates of convergence in the sup-norm as well as adaptive estimation of local M-estimators which might be of some independent interest, and which can also be applied in various other settings. We investigate the finite-sample behaviour of our method in a simulation study, and give an illustration to a real data set from bioinformatics.

Gwenaëlle Castellan, Anthony Cousien, Viet Chi Tran.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 50--81.

Abstract:
Global sensitivity analysis is a set of methods aiming at quantifying the contribution of an uncertain input parameter of the model (or combination of parameters) on the variability of the response. We consider here the estimation of the Sobol indices of order 1 which are commonly-used indicators based on a decomposition of the output’s variance. In a deterministic framework, when the same inputs always give the same outputs, these indices are usually estimated by replicated simulations of the model. In a stochastic framework, when the response given a set of input parameters is not unique due to randomness in the model, metamodels are often used to approximate the mean and dispersion of the response by deterministic functions. We propose a new non-parametric estimator without the need of defining a metamodel to estimate the Sobol indices of order 1. The estimator is based on warped wavelets and is adaptive in the regularity of the model. The convergence of the mean square error to zero, when the number of simulations of the model tend to infinity, is computed and an elbow effect is shown, depending on the regularity of the model. Applications in Epidemiology are carried to illustrate the use of non-parametric estimators.

Fabien Panloup, Samy Tindel, Maylis Varvenne.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1075--1136.

Abstract:
In this paper we consider the drift estimation problem for a general differential equation driven by an additive multidimensional fractional Brownian motion, under ergodic assumptions on the drift coefficient. Our estimation procedure is based on the identification of the invariant measure, and we provide consistency results as well as some information about the convergence rate. We also give some examples of coefficients for which the identifiability assumption for the invariant measure is satisfied.

We study the least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space as a special case. We first investigate regularized algorithms adapted to a projection operator on a closed subspace of the Hilbert space. We prove convergence results with respect to variants of norms, under a capacity assumption on the hypothesis space and a regularity condition on the target function. As a result, we obtain optimal rates for regularized algorithms with randomized sketches, provided that the sketch dimension is proportional to the effective dimension up to a logarithmic factor. As a byproduct, we obtain similar results for Nystr"{o}m regularized algorithms. Our results provide optimal, distribution-dependent rates that do not have any saturation effect for sketched/Nystr"{o}m regularized algorithms, considering both the attainable and non-attainable cases, in the well-conditioned regimes. We then study stochastic gradient methods with projection over the subspace, allowing multi-pass over the data and minibatches, and we derive similar optimal statistical convergence results.

We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving noise and reward feedback. Our main theoretical result provides an explicit bound on the sample or evaluation complexity: we show that these methods are guaranteed to converge to within any pre-specified tolerance of the optimal policy with a number of zero-order evaluations that is an explicit polynomial of the error tolerance, dimension, and curvature properties of the problem. Our analysis reveals some interesting differences between the settings of additive driving noise and random initialization, as well as the settings of one-point and two-point reward feedback. Our theory is corroborated by simulations of derivative-free methods in application to these systems. Along the way, we derive convergence rates for stochastic zero-order optimization algorithms when applied to a certain class of non-convex problems.

We propose graph-dependent implicit regularisation strategies for synchronised distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity, and smoothness, we establish statistical learning rates that retain, up to logarithmic terms, single-machine serial statistical guarantees through implicit regularisation (step size tuning and early stopping) with appropriate dependence on the graph topology. Our approach avoids the need for explicit regularisation in decentralised learning problems, such as adding constraints to the empirical risk minimisation rule. Particularly for distributed methods, the use of implicit regularisation allows the algorithm to remain simple, without projections or dual methods. To prove our results, we establish graph-independent generalisation bounds for Distributed SGD that match the single-machine serial SGD setting (using algorithmic stability), and we establish graph-dependent optimisation bounds that are of independent interest. We present numerical experiments to show that the qualitative nature of the upper bounds we derive can be representative of real behaviours.

We present a probabilistic framework for studying adversarial attacks on discrete data. Based on this framework, we derive a perturbation-based method, Greedy Attack, and a scalable learning-based method, Gumbel Attack, that illustrate various tradeoffs in the design of attacks. We demonstrate the effectiveness of these methods using both quantitative metrics and human evaluation on various state-of-the-art models for text classification, including a word-based CNN, a character-based CNN and an LSTM. As an example of our results, we show that the accuracy of character-based convolutional networks drops to the level of random selection by modifying only five characters through Greedy Attack.

In this paper we introduce a statistical model, called additively faithful directed acyclic graph (AFDAG), for causal learning from observational data. Our approach is based on additive conditional independence (ACI), a recently proposed three-way statistical relation that shares many similarities with conditional independence but without resorting to multi-dimensional kernels. This distinct feature strikes a balance between a parametric model and a fully nonparametric model, which makes the proposed model attractive for handling large networks. We develop an estimator for AFDAG based on a linear operator that characterizes ACI, and establish the consistency and convergence rates of this estimator, as well as the uniform consistency of the estimated DAG. Moreover, we introduce a modified PC-algorithm to implement the estimating procedure efficiently, so that its complexity is determined by the level of sparseness rather than the dimension of the network. Through simulation studies we show that our method outperforms existing methods when commonly assumed conditions such as Gaussian or Gaussian copula distributions do not hold. Finally, the usefulness of AFDAG formulation is demonstrated through an application to a proteomics data set.

We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates (or sums) across actions when estimating the gradient, instead of relying only on the action in the sampled trajectory. For continuous action spaces, we first derive a practical result for Gaussian policies and quadratic critics and then extend it to a universal analytical method, covering a broad class of actors and critics, including Gaussian, exponential families, and policies with bounded support. For Gaussian policies, we introduce an exploration method that uses covariance proportional to the matrix exponential of the scaled Hessian of the critic with respect to the actions. For discrete action spaces, we derive a variant of EPG based on softmax policies. We also establish a new general policy gradient theorem, of which the stochastic and deterministic policy gradient theorems are special cases. Furthermore, we prove that EPG reduces the variance of the gradient estimates without requiring deterministic policies and with little computational overhead. Finally, we provide an extensive experimental evaluation of EPG and show that it outperforms existing approaches on multiple challenging control domains.

Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large datasets require to resort to approximations. In this work, the computation of the least-squares prediction is itself treated as a probabilistic inference problem. We propose a structured Gaussian regression model on the kernel function that uses projections of the kernel matrix to obtain a low-rank approximation of the kernel and the matrix. A central result is an enhanced way to use the method of conjugate gradients for the specific setting of least-squares regression as encountered in machine learning.