Simultaneous Parameter Learning and Bi-Clustering for Multi-Response Models

We consider multi-response and multitask regression models, where the parameter matrix to be estimated is expected to have an unknown grouping structure. The groupings can be along tasks, or features, or both, the last one indicating a bi-cluster or "checkerboard" structure. Discovering this grouping structure along with parameter inference makes sense in several applications, such as multi-response Genome-Wide Association Studies. This additional structure can not only can be leveraged for more accurate parameter estimation, but it also provides valuable information on the underlying data mechanisms (e.g. relationships among genotypes and phenotypes in GWAS). In this paper, we propose two formulations to simultaneously learn the parameter matrix and its group structures, based on convex regularization penalties. We present optimization approaches to solve the resulting problems and provide numerical convergence guarantees. Our approaches are validated on extensive simulations and real datasets concerning phenotypes and genotypes of plant varieties.Comment: 15 pages, 15 figure

Modelling of temporal fluctuation scaling in online news network with independent cascade model

We show that activity of online news outlets follows a temporal fluctuation scaling law and we recover this feature using an independent cascade model augmented with a varying hype parameter representing a viral potential of an original article. We use the Event Registry platform to track activity of over 10,000 news outlets in 11 different topics in the course of the year 2016. Analyzing over 22,000,000 articles, we found that fluctuation scaling exponents $\alpha$ depend on time window size $\Delta$ in a characteristic way for all the considered topics -- news outlets activities are partially synchronized for $\Delta>15\mathrm{min}$ with a cross-over for $\Delta=1\mathrm{day}$. The proposed model was run on several synthetic network models as well as on a network extracted from the real data. Our approach discards timestamps as not fully reliable observables and focuses on co-occurrences of publishers in cascades of similarly phrased news items. We make use of the Event Registry news clustering feature to find correlations between content published by news outlets in order to uncover common information propagation paths in published articles and to estimate weights of edges in the independent cascade model. While the independent cascade model follows the fluctuation scaling law with a trivial exponent $\alpha=0.5$, we argue that besides the topology of the underlying cooperation network a temporal clustering of articles with similar hypes is necessary to qualitatively reproduce the fluctuation scaling observed in the data

Learning Influence-Receptivity Network Structure with Guarantee

Traditional works on community detection from observations of information cascade assume that a single adjacency matrix parametrizes all the observed cascades. However, in reality the connection structure usually does not stay the same across cascades. For example, different people have different topics of interest, therefore the connection structure depends on the information/topic content of the cascade. In this paper we consider the case where we observe a sequence of noisy adjacency matrices triggered by information/event with different topic distributions. We propose a novel latent model using the intuition that a connection is more likely to exist between two nodes if they are interested in similar topics, which are common with the information/event. Specifically, we endow each node with two node-topic vectors: an influence vector that measures how influential/authoritative they are on each topic; and a receptivity vector that measures how receptive/susceptible they are to each topic. We show how these two node-topic structures can be estimated from observed adjacency matrices with theoretical guarantee on estimation error, in cases where the topic distributions of the information/event are known, as well as when they are unknown. Experiments on synthetic and real data demonstrate the effectiveness of our model and superior performance compared to state-of-the-art methods

Constrained High Dimensional Statistical Inference

In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained. However, in many problems, there are natural constraints on model parameters and one is interested in whether the parameters are on the boundary of the constraint or not. e.g. non-negativity constraints for transmission rates in network diffusion. In this paper, we provide algorithms to solve this problem of hypothesis testing in high-dimensional statistical models under constrained parameter space. We show that following our testing procedure we are able to get asymptotic designed Type I error under the null. Numerical experiments demonstrate that our algorithm has greater power than the standard algorithms where the constraints are ignored. We demonstrate the effectiveness of our algorithms on two real datasets where we have {\emph{intrinsic}} constraint on the parameters

Tensor Canonical Correlation Analysis with Convergence and Statistical Guarantees

In many applications, such as classification of images or videos, it is of interest to develop a framework for tensor data instead of an ad-hoc way of transforming data to vectors due to the computational and under-sampling issues. In this paper, we study convergence and statistical properties of two-dimensional canonical correlation analysis \citep{Lee2007Two} under an assumption that data come from a probabilistic model. We show that carefully initialized the power method converges to the optimum and provide a finite sample bound. Then we extend this framework to tensor-valued data and propose the higher-order power method, which is commonly used in tensor decomposition, to extract the canonical directions. Our method can be used effectively in a large-scale data setting by solving the inner least squares problem with a stochastic gradient descent, and we justify convergence via the theory of Lojasiewicz's inequalities without any assumption on data generating process and initialization. For practical applications, we further develop (a) an inexact updating scheme which allows us to use the state-of-the-art stochastic gradient descent algorithm, (b) an effective initialization scheme which alleviates the problem of local optimum in non-convex optimization, and (c) a deflation procedure for extracting several canonical components. Empirical analyses on challenging data including gene expression and air pollution indexes in Taiwan, show the effectiveness and efficiency of the proposed methodology. Our results fill a missing, but crucial, part in the literature on tensor data