Minimax Quasi-Bayesian estimation in sparse canonical correlation analysis via a Rayleigh quotient function

Canonical correlation analysis (CCA) is a popular statistical technique for exploring the relationship between datasets. The estimation of sparse canonical correlation vectors has emerged in recent years as an important but challenging variation of the CCA problem, with widespread applications. Currently available rate-optimal estimators for sparse canonical correlation vectors are expensive to compute. We propose a quasi-Bayesian estimation procedure that achieves the minimax estimation rate, and yet is easy to compute by Markov Chain Monte Carlo (MCMC). The method builds on ([37]) and uses a re-scaled Rayleigh quotient function as a quasi-log-likelihood. However unlike these authors, we adopt a Bayesian framework that combines this quasi-log-likelihood with a spike-and-slab prior that serves to regularize the inference and promote sparsity. We investigated the empirical behavior of the proposed method on both continuous and truncated data, and we noted that it outperforms several state-of-the-art methods. As an application, we use the methodology to maximally correlate clinical variables and proteomic data for a better understanding of covid-19 disease

Red Queen Competition through Innovations on a Digital Platform for Experience Goods

This study examines a dynamic process of competition, learning, and innovation, referred to as Red Queen, on a digital platform for trading experience goods. Specifically, by analyzing the package tours sold by 114 travel agencies on the world\u27s largest online travel platform - Trip.com, the study reveals initial evidence of Red Queen as a type of intra-platform competition and how it is played out by firms through continuous innovations. The findings suggest that the providers of experience goods, on a digital platform without intellectual property protection, should maintain appropriate innovation postures according to the type of innovations and level of rivalry in the markets. High performance may result from leading postures for incremental innovations, and from middle-of-the-road postures for radical innovations, especially in high-rivalry markets. These findings can help experience goods providers strategize what, how, and where to innovate in order to beat competition and improve performance on digital platforms

The Relationship between Product Innovation and Online Sales: A Red Queen Competition Perspective

Competitions among online sellers on an e-commerce platforms has entered the era of “Red sea”. The highly transparent feature reduces the costs of learning and imitation, which breeds vicious competition on markets and increases product similarity. Hence, online sellers have to promote product iteration and innovation to meet the changes of market demands. However, how to measure the product innovative of online sellers, as well as the relationship between the posture of product innovation and online sales in changing competitive environment have barely been empirically revealed. This study intends to theoretical analyze the relationship between the posture of two different types of product innovation and online sales grounded on the red queen competition theory. The expected results are: First, compared with the average level of the industry, the better the posture of updated product innovation is, the higher the online sales are. Second, compared with the average level of the industry, the relationship between the posture of new product innovation and online sales is inversely U-shaped. This study not only expands the research scope on organizational competition mechanism based on the red queen competition theory, but also provides essential ideas for online sellers to develop product innovation strategies in competitive environments

A statistical perspective on algorithm unrolling models for inverse problems

We consider inverse problems where the conditional distribution of the observation ${\bf y}$ given the latent variable of interest ${\bf x}$ (also known as the forward model) is known, and we have access to a data set in which multiple instances of ${\bf x}$ and ${\bf y}$ are both observed. In this context, algorithm unrolling has become a very popular approach for designing state-of-the-art deep neural network architectures that effectively exploit the forward model. We analyze the statistical complexity of the gradient descent network (GDN), an algorithm unrolling architecture driven by proximal gradient descent. We show that the unrolling depth needed for the optimal statistical performance of GDNs is of order $\log(n)/\log(\varrho_n^{-1})$, where $n$ is the sample size, and $\varrho_n$ is the convergence rate of the corresponding gradient descent algorithm. We also show that when the negative log-density of the latent variable ${\bf x}$ has a simple proximal operator, then a GDN unrolled at depth $D'$ can solve the inverse problem at the parametric rate $O(D'/\sqrt{n})$. Our results thus also suggest that algorithm unrolling models are prone to overfitting as the unrolling depth $D'$ increases. We provide several examples to illustrate these results

Transfer Learning for Context-Aware Spoken Language Understanding

Spoken language understanding (SLU) is a key component of task-oriented dialogue systems. SLU parses natural language user utterances into semantic frames. Previous work has shown that incorporating context information significantly improves SLU performance for multi-turn dialogues. However, collecting a large-scale human-labeled multi-turn dialogue corpus for the target domains is complex and costly. To reduce dependency on the collection and annotation effort, we propose a Context Encoding Language Transformer (CELT) model facilitating exploiting various context information for SLU. We explore different transfer learning approaches to reduce dependency on data collection and annotation. In addition to unsupervised pre-training using large-scale general purpose unlabeled corpora, such as Wikipedia, we explore unsupervised and supervised adaptive training approaches for transfer learning to benefit from other in-domain and out-of-domain dialogue corpora. Experimental results demonstrate that the proposed model with the proposed transfer learning approaches achieves significant improvement on the SLU performance over state-of-the-art models on two large-scale single-turn dialogue benchmarks and one large-scale multi-turn dialogue benchmark.Comment: 6 pages, 3 figures, ASRU201

Push–pull type manganese (III) corroles

The synthesis of three low symmetry A2B type Mn(III)triarylcorroles with meso-aryl substituents that provide push–pull electron-donating and -withdrawing properties is reported. An analysis of the structure-property relationships for the optical and redox properties has been carried out through a comparison with the results of theoretical calculations. The results demonstrate that A2B type Mn(III)triarylcorroles interact strongly with cell-free circulating tumor deoxyribonucleic acid (ctDNA) in solution, and that the interaction constants are enhanced when a stronger electron-donating substituent is introduced at the 10-position of the meso-triarylcorrole ligand

(Local) Non-Asymptotic Analysis of Logistic Fictitious Play for Two-Player Zero-Sum Games and Its Deterministic Variant

We conduct a local non-asymptotic analysis of the logistic fictitious play (LFP) algorithm, and show that with high probability, this algorithm converges locally at rate $O(1/t)$. To achieve this, we first develop a global non-asymptotic analysis of the deterministic variant of LFP, which we call DLFP, and derive a class of convergence rates based on different step-sizes. We then incorporate a particular form of stochastic noise to the analysis of DLFP, and obtain the local convergence rate of LFP. As a result of independent interest, we extend DLFP to solve a class of strongly convex composite optimization problems. We show that although the resulting algorithm is a simple variant of the generalized Frank-Wolfe method in Nesterov [1,Section 5], somewhat surprisingly, it enjoys significantly improved convergence rate.Comment: 12 page