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The search for new gravity-like interactions at the sub-millimeter scale is a compelling area of research, with important implications for the understanding of classical gravity and its connections with quantum physics. We report improved constraints on Yukawa-type interactions in the $10\,\mathrm{\mu m}$ regime using optically levitated dielectric microspheres as test masses. The search is performed, for the first time, sensing multiple spatial components of the force vector, and with sensitivity improved by a factor of $\sim 100$ with respect to previous measurements using the same technique. The resulting upper limit on the strength of a hypothetical new force is $10^7$ at a Yukawa range $\lambda\simeq 5\;\mu$m and close to $10^6$ for $\lambda \gtrsim 10\;\mu$m. This result also advances our efforts to measure gravitational effects using micrometer-size objects, with important implications for embryonic ideas to investigate the quantum nature of gravity.

Stochastic approximation (SA) is a powerful and scalable computational method for iteratively estimating the solution of optimization problems in the presence of randomness, particularly well-suited for large-scale and streaming data settings. In this work, we propose a theoretical framework for stochastic approximation (SA) applied to non-parametric least squares in reproducing kernel Hilbert spaces (RKHS), enabling online statistical inference in non-parametric regression models. We achieve this by constructing asymptotically valid pointwise (and simultaneous) confidence intervals (bands) for local (and global) inference of the nonlinear regression function, via employing an online multiplier bootstrap approach to functional stochastic gradient descent (SGD) algorithm in the RKHS. Our main theoretical contributions consist of a unified framework for characterizing the non-asymptotic behavior of the functional SGD estimator and demonstrating the consistency of the multiplier bootstrap method. The proof techniques involve the development of a higher-order expansion of the functional SGD estimator under the supremum norm metric and the Gaussian approximation of suprema of weighted and non-identically distributed empirical processes. Our theory specifically reveals an interesting relationship between the tuning of step sizes in SGD for estimation and the accuracy of uncertainty quantification.

Mapping of human brain structural connectomes via diffusion MRI offers a unique opportunity to understand brain structural connectivity and relate it to various human traits, such as cognition. However, head displacement during image acquisition can compromise the accuracy of connectome reconstructions and subsequent inference results. We develop a generative model to learn low-dimensional representations of structural connectomes invariant to motion-induced artifacts, so that we can link brain networks and human traits more accurately, and generate motion-adjusted connectomes. We apply the proposed model to data from the Adolescent Brain Cognitive Development (ABCD) study and the Human Connectome Project (HCP) to investigate how our motion-invariant connectomes facilitate understanding of the brain network and its relationship with cognition. Empirical results demonstrate that the proposed motion-invariant variational auto-encoder (inv-VAE) outperforms its competitors in various aspects. In particular, motion-adjusted structural connectomes are more strongly associated with a wide array of cognition-related traits than other approaches without motion adjustment.

Conformal prediction aims to determine precise levels of confidence in predictions for new objects using past experience. However, the commonly used exchangeable assumptions between the training data and testing data limit its usage in dealing with contaminated testing sets. In this paper, we develop a novel flow-based conformal inference (FCI) method to build predictive sets and infer outliers for complex and high-dimensional data. We leverage ideas from adversarial flow to transfer the input data to a random vector with known distributions. Our roundtrip transformation can map the input data to a low-dimensional space, meanwhile reserving the conditional distribution of input data given each class label, which enables us to construct a non-conformity score for uncertainty quantification. Our approach is applicable and robust when the testing data is contaminated. We evaluate our method, robust flow-based conformal inference, on benchmark datasets. We find that it produces effective predictive sets and accurate outlier detection and is more powerful relative to competing approaches.

Embedding is a useful technique to project a high-dimensional feature into a low-dimensional space, and it has many successful applications including link prediction, node classification and natural language processing. Current approaches mainly focus on static data, which usually lead to unsatisfactory performance in applications involving large changes over time. How to dynamically characterize the variation of the embedded features is still largely unexplored. In this paper, we introduce a dynamic variational embedding (DVE) approach for sequence-aware data based on recent advances in recurrent neural networks. DVE can model the node's intrinsic nature and temporal variation explicitly and simultaneously, which are crucial for exploration. We further apply DVE to sequence-aware recommender systems, and develop an end-to-end neural architecture for link prediction.

Recent years have witnessed rapid developments on collaborative filtering techniques for improving the performance of recommender systems due to the growing need of companies to help users discover new and relevant items. However, the majority of existing literature focuses on delivering items which match the user model learned from users' past preferences. A good recommendation model is expected to recommend items that are known to enjoy and items that are novel to try. In this work, we introduce an exploitation-exploration motivated variational auto-encoder (XploVAE) to collaborative filtering. To facilitate personalized recommendations, we construct user-specific subgraphs, which contain the first-order proximity capturing observed user-item interactions for exploitation and the high-order proximity for exploration. A hierarchical latent space model is utilized to learn the personalized item embedding for a given user, along with the population distribution of all user subgraphs. Finally, experimental results on various real-world datasets clearly demonstrate the effectiveness of our proposed model on leveraging the exploitation and exploration recommendation tasks., Comment: 9 pages, 6 figures

When there is a distributional shift between data used to train a predictive algorithm and current data, performance can suffer. This is known as the domain adaptation problem. Bootstrap aggregating, or bagging, is a popular method for improving stability of predictive algorithms, while reducing variance and protecting against over-fitting. This article proposes a domain adaptive bagging method coupled with a new iterative nearest neighbor sampler. The key idea is to draw bootstrap samples from the training data in such a manner that their distribution equals that of new testing data. The proposed approach provides a general ensemble framework that can be applied to arbitrary classifiers. We further modify the method to allow anomalous samples in the test data corresponding to outliers in the training data. Theoretical support is provided, and the approach is compared to alternatives in simulations and real data applications.

There has been huge interest in studying human brain connectomes inferred from different imaging modalities and exploring their relationship with human traits, such as cognition. Brain connectomes are usually represented as networks, with nodes corresponding to different regions of interest (ROIs) and edges to connection strengths between ROIs. Due to the high-dimensionality and non-Euclidean nature of networks, it is challenging to depict their population distribution and relate them to human traits. Current approaches focus on summarizing the network using either pre-specified topological features or principal components analysis (PCA). In this paper, building on recent advances in deep learning, we develop a nonlinear latent factor model to characterize the population distribution of brain graphs and infer the relationships between brain structural connectomes and human traits. We refer to our method as Graph AuTo-Encoding (GATE). We applied GATE to two large-scale brain imaging datasets, the Adolescent Brain Cognitive Development (ABCD) study and the Human Connectome Project (HCP) for adults, to understand the structural brain connectome and its relationship with cognition. Numerical results demonstrate huge advantages of GATE over competitors in terms of prediction accuracy, statistical inference and computing efficiency. We found that structural connectomes have a stronger association with a wide range of human cognitive traits than was apparent using previous approaches., Comment: 31 pages, 12 figures, 5 tables

In this paper, we propose a random projection approach to estimate variance in kernel ridge regression. Our approach leads to a consistent estimator of the true variance, while being computationally more efficient. Our variance estimator is optimal for a large family of kernels, including cubic splines and Gaussian kernels. Simulation analysis is conducted to support our theory., Comment: To Appear in 2018 Allerton

This paper aims to solve a basic problem in distributed statistical inference: how many machines can we use in parallel computing? In kernel ridge regression, we address this question in two important settings: nonparametric estimation and hypothesis testing. Specifically, we find a range for the number of machines under which optimal estimation/testing is achievable. The employed empirical processes method provides a unified framework, that allows us to handle various regression problems (such as thin-plate splines and nonparametric additive regression) under different settings (such as univariate, multivariate and diverging-dimensional designs). It is worth noting that the upper bounds of the number of machines are proven to be un-improvable (upto a logarithmic factor) in two important cases: smoothing spline regression and Gaussian RKHS regression. Our theoretical findings are backed by thorough numerical studies., Comment: This work extends the work in arXiv:1512.09226 to random and multivariate design

Early stopping of iterative algorithms is an algorithmic regularization method to avoid over-fitting in estimation and classification. In this paper, we show that early stopping can also be applied to obtain the minimax optimal testing in a general non-parametric setup. Specifically, a Wald-type test statistic is obtained based on an iterated estimate produced by functional gradient descent algorithms in a reproducing kernel Hilbert space. A notable contribution is to establish a "sharp" stopping rule: when the number of iterations achieves an optimal order, testing optimality is achievable; otherwise, testing optimality becomes impossible. As a by-product, a similar sharpness result is also derived for minimax optimal estimation under early stopping studied in [11] and [19]. All obtained results hold for various kernel classes, including Sobolev smoothness classes and Gaussian kernel classes., Comment: To appear in NIPS 2018

A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the specific kernel ridge regression setup, a simple distance-based test statistic is proposed. Notably, we derive the minimum number of random projections that is sufficient for achieving testing optimality in terms of the minimax rate. An adaptive testing procedure is further established without prior knowledge of regularity. One technical contribution is to establish upper bounds for a range of tail sums of empirical kernel eigenvalues. Simulations and real data analysis are conducted to support our theory.