Nonparametric, tuning-free estimation of S-shaped functions

We consider the nonparametric estimation of an S-shaped regression function. The least squares estimator provides a very natural, tuning-free approach, but results in a non-convex optimisation problem, since the inflection point is unknown. We show that the estimator may nevertheless be regarded as a projection onto a finite union of convex cones, which allows us to propose a mixed primal-dual bases algorithm for its efficient, sequential computation. After developing a projection framework that demonstrates the consistency and robustness to misspecification of the estimator, our main theoretical results provide sharp oracle inequalities that yield worst-case and adaptive risk bounds for the estimation of the regression function, as well as a rate of convergence for the estimation of the inflection point. These results reveal not only that the estimator achieves the minimax optimal rate of convergence for both the estimation of the regression function and its inflection point (up to a logarithmic factor in the latter case), but also that it is able to achieve an almost-parametric rate when the true regression function is piecewise affine with not too many affine pieces. Simulations and a real data application to air pollution modelling also confirm the desirable finite-sample properties of the estimator, and our algorithm is implemented in the R package Sshaped.

Shuffle Transformer with Feature Alignment for Video Face Parsing

This is a short technical report introducing the solution of the Team TCParser for Short-video Face Parsing Track of The 3rd Person in Context (PIC) Workshop and Challenge at CVPR 2021. In this paper, we introduce a strong backbone which is cross-window based Shuffle Transformer for presenting accurate face parsing representation. To further obtain the finer segmentation results, especially on the edges, we introduce a Feature Alignment Aggregation (FAA) module. It can effectively relieve the feature misalignment issue caused by multi-resolution feature aggregation. Benefiting from the stronger backbone and better feature aggregation, the proposed method achieves 86.9519% score in the Short-video Face Parsing track of the 3rd Person in Context (PIC) Workshop and Challenge, ranked the first place.

Deep-AIR: A Hybrid CNN-LSTM Framework for Air Quality Modeling in Metropolitan Cities

Air pollution has long been a serious environmental health challenge, especially in metropolitan cities, where air pollutant concentrations are exacerbated by the street canyon effect and high building density. Whilst accurately monitoring and forecasting air pollution are highly crucial, existing data-driven models fail to fully address the complex interaction between air pollution and urban dynamics. Our Deep-AIR, a novel hybrid deep learning framework that combines a convolutional neural network with a long short-term memory network, aims to address this gap to provide fine-grained city-wide air pollution estimation and station-wide forecast. Our proposed framework creates 1x1 convolution layers to strengthen the learning of cross-feature spatial interaction between air pollution and important urban dynamic features, particularly road density, building density/height, and street canyon effect. Using Hong Kong and Beijing as case studies, Deep-AIR achieves a higher accuracy than our baseline models. Our model attains an accuracy of 67.6%, 77.2%, and 66.1% in fine-grained hourly estimation, 1-hr, and 24-hr air pollution forecast for Hong Kong, and an accuracy of 65.0%, 75.3%, and 63.5% for Beijing. Our saliency analysis has revealed that for Hong Kong, street canyon and road density are the best estimators for NO2, while meteorology is the best estimator for PM2.5.

Multiplier U-processes: sharp bounds and applications

The theory for multiplier empirical processes has been one of the central topics in the development of the classical theory of empirical processes, due to its wide applicability to various statistical problems. In this paper, we develop theory and tools for studying multiplier $U$-processes, a natural higher-order generalization of the multiplier empirical processes. To this end, we develop a multiplier inequality that quantifies the moduli of continuity of the multiplier $U$-process in terms of that of the (decoupled) symmetrized $U$-process. The new inequality finds a variety of applications including (i) multiplier and bootstrap central limit theorems for $U$-processes, (ii) general theory for bootstrap $M$-estimators based on $U$-statistics, and (iii) theory for $M$-estimation under general complex sampling designs, again based on $U$-statistics.

Evaluating the Discrimination Ability of Proper Multivariate Scoring Rules

Proper scoring rules are commonly applied to quantify the accuracy of distribution forecasts. Given an observation they assign a scalar score to each distribution forecast, with the the lowest expected score attributed to the true distribution. The energy and variogram scores are two rules that have recently gained some popularity in multivariate settings because their computation does not require a forecast to have parametric density function and so they are broadly applicable. Here we conduct a simulation study to compare the discrimination ability between the energy score and three variogram scores. Compared with other studies, our simulation design is more realistic because it is supported by a historical data set containing commodity prices, currencies and interest rates, and our data generating processes include a diverse selection of models with different marginal distributions, dependence structure, and calibration windows. This facilitates a comprehensive comparison of the performance of proper scoring rules in different settings. To compare the scores we use three metrics: the mean relative score, error rate and a generalised discrimination heuristic. Overall, we find that the variogram score with parameter p=0.5 outperforms the energy score and the other two variogram scores.

A general method for power analysis in testing high dimensional covariance matrices

Covariance matrix testing for high dimensional data is a fundamental problem. A large class of covariance test statistics based on certain averaged spectral statistics of the sample covariance matrix are known to obey central limit theorems under the null. However, precise understanding for the power behavior of the corresponding tests under general alternatives remains largely unknown. This paper develops a general method for analyzing the power behavior of covariance test statistics via accurate non-asymptotic power expansions. We specialize our general method to two prototypical settings of testing identity and sphericity, and derive sharp power expansion for a number of widely used tests, including the likelihood ratio tests, Ledoit-Nagao-Wolfs test, Cai-Mas test and Johns test. The power expansion for each of those tests holds uniformly over all possible alternatives under mild growth conditions on the dimension-to-sample ratio. Interestingly, although some of those tests are previously known to share the same limiting power behavior under spiked covariance alternatives with a fixed number of spikes, our new power characterizations indicate that such equivalence fails when many spikes exist. The proofs of our results combine techniques from Poincare-type inequalities, random matrices and zonal polynomials.

Unraveling Ultrafast Photoionization in Hexagonal Boron Nitride

The non-linear response of dielectrics to intense, ultrashort electric fields has been a sustained topic of interest for decades with one of its most important applications being femtosecond laser micro/nano-machining. More recently, renewed interests in strong field physics of solids were raised with the advent of mid-infrared femtosecond laser pulses, such as high-order harmonic generation, optical-field-induced currents, etc. All these processes are underpinned by photoionization (PI), namely the electron transfer from the valence to the conduction bands, on a time scale too short for phononic motion to be of relevance. Here, in hexagonal boron nitride, we reveal that the bandgap can be finely manipulated by femtosecond laser pulses as a function of field polarization direction with respect to the lattice, in addition to the fields intensity. It is the modification of bandgap that enables the ultrafast PI processes to take place in dielectrics. We further demonstrate the validity of the Keldysh theory in describing PI in dielectrics in the few TW/cm2 regime.

Symmetry criteria for Hochschild extensions

We give two sufficient and necessary conditions for a Hochschild extension of a finite dimensional algebra by its dual bimodule and a Hochschild 2-cocycle to be a symmetric algebra.

Earliest Resolution to the Neutrino Mass Ordering?

We hereby illustrate and numerically demonstrate via a simplified proof of concept calculation tuned to the latest average neutrino global data that the combined sensitivity of JUNO with NOvA and T2K experiments has the potential to be the first fully resolved ($geq$5$sigma$) measurement of neutrino Mass Ordering (MO) around 2028; tightly linked to the JUNO schedule. Our predictions account for the key ambiguities and the most relevant $pm$1$sigma$ data fluctuations. In the absence of any concrete MO theoretical prediction and given its intrinsic binary outcome, we highlight the benefits of having such a resolved measurement in the light of the remarkable MO resolution ability of the next generation of long baseline neutrino beams experiments. We motivate the opportunity of exploiting the MO experimental framework to scrutinise the standard oscillation model, thus, opening for unique discovery potential, should unexpected discrepancies manifest. Phenomenologically, the deepest insight relies on the articulation of MO resolved measurements via at least the two possible methodologies matter effects and purely vacuum oscillations. Thus, we argue that the JUNO vacuum MO measurement may feasibly yield full resolution in combination to the next generation of long baseline neutrino beams experiments.

Complex sampling designs: uniform limit theorems and applications

In this paper, we develop a general approach to proving global and local uniform limit theorems for the Horvitz-Thompson empirical process arising from complex sampling designs. Global theorems such as Glivenko-Cantelli and Donsker theorems, and local theorems such as local asymptotic modulus and related ratio-type limit theorems are proved for both the Horvitz-Thompson empirical process, and its calibrated version. Limit theorems of other variants and their condition