Chuyang Ke

Chuyang Ke, Jean Honorio

In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.

Site Bai, Chuyang Ke, Jean Honorio

We propose the framework of dual convexified convolutional neural networks (DCCNNs). In this framework, we first introduce a primal learning problem motivated by convexified convolutional neural networks (CCNNs), and then construct the dual convex training program through careful analysis of the Karush-Kuhn-Tucker (KKT) conditions and Fenchel conjugates. Our approach reduces the computational overhead of constructing a large kernel matrix and more importantly, eliminates the ambiguity of factorizing the matrix. Due to the low-rank structure in CCNNs and the related subdifferential of nuclear norms, there is no closed-form expression to recover the primal solution from the dual solution. To overcome this, we propose a highly novel weight recovery algorithm, which takes the dual solution and the kernel information as the input, and recovers the linear weight and the output of convolutional layer, instead of weight parameter. Furthermore, our recovery algorithm exploits the low-rank structure and imposes a small number of filters indirectly, which reduces the parameter size. As a result, DCCNNs inherit all the statistical benefits of CCNNs, while enjoying a more formal and efficient workflow.

Chuyang Ke, Jean Honorio

We study the problem of consistently recovering the sparsity pattern of a regression parameter vector from correlated observations governed by deterministic missing data patterns using Lasso. We consider the case in which the observed dataset is censored by a deterministic, non-uniform filter. Recovering the sparsity pattern in datasets with deterministic missing structure can be arguably more challenging than recovering in a uniformly-at-random scenario. In this paper, we propose an efficient algorithm for missing value imputation by utilizing the topological property of the censorship filter. We then provide novel theoretical results for exact recovery of the sparsity pattern using the proposed imputation strategy. Our analysis shows that, under certain statistical and topological conditions, the hidden sparsity pattern can be recovered consistently with high probability in polynomial time and logarithmic sample complexity.

Chuyang Ke, Jean Honorio

In this paper, we examine the problem of partial inference in the context of structured prediction. Using a generative model approach, we consider the task of maximizing a score function with unary and pairwise potentials in the space of labels on graphs. Employing a two-stage convex optimization algorithm for label recovery, we analyze the conditions under which a majority of the labels can be recovered. We introduce a novel perspective on the Karush-Kuhn-Tucker (KKT) conditions and primal and dual construction, and provide statistical and topological requirements for partial recovery with provable guarantees.

Chuyang Ke, Jean Honorio

In this paper, we study the problem of recovering the community structure of a network under federated myopic learning. Under this paradigm, we have several clients, each of them having a myopic view, i.e., observing a small subgraph of the network. Each client sends a censored evidence graph to a central server. We provide an efficient algorithm, which computes a consensus signed weighted graph from clients evidence, and recovers the underlying network structure in the central server. We analyze the topological structure conditions of the network, as well as the signal and noise levels of the clients that allow for recovery of the network structure. Our analysis shows that exact recovery is possible and can be achieved in polynomial time. We also provide information-theoretic limits for the central server to recover the network structure from any single client evidence. Finally, as a byproduct of our analysis, we provide a novel Cheeger-type inequality for general signed weighted graphs.

Kevin Bello, Chuyang Ke, Jean Honorio

Performing inference in graphs is a common task within several machine learning problems, e.g., image segmentation, community detection, among others. For a given undirected connected graph, we tackle the statistical problem of exactly recovering an unknown ground-truth binary labeling of the nodes from a single corrupted observation of each edge. Such problem can be formulated as a quadratic combinatorial optimization problem over the boolean hypercube, where it has been shown before that one can (with high probability and in polynomial time) exactly recover the ground-truth labeling of graphs that have an isoperimetric number that grows with respect to the number of nodes (e.g., complete graphs, regular expanders). In this work, we apply a powerful hierarchy of relaxations, known as the sum-of-squares (SoS) hierarchy, to the combinatorial problem. Motivated by empirical evidence on the improvement in exact recoverability, we center our attention on the degree-4 SoS relaxation and set out to understand the origin of such improvement from a graph theoretical perspective. We show that the solution of the dual of the relaxed problem is related to finding edge weights of the Johnson and Kneser graphs, where the weights fulfill the SoS constraints and intuitively allow the input graph to increase its algebraic connectivity. Finally, as byproduct of our analysis, we derive a novel Cheeger-type lower bound for the algebraic connectivity of graphs with signed edge weights.

Jiajun Liang, Chuyang Ke, Jean Honorio

In this paper, we study the information theoretic bounds for exact recovery in sub-hypergraph models for community detection. We define a general model called the $m-$uniform sub-hypergraph stochastic block model ($m-$ShSBM). Under the $m-$ShSBM, we use Fano's inequality to identify the region of model parameters where any algorithm fails to exactly recover the planted communities with a large probability. We also identify the region where a Maximum Likelihood Estimation (MLE) algorithm succeeds to exactly recover the communities with high probability. Our bounds are tight and pertain to the community detection problems in various models such as the planted hypergraph stochastic block model, the planted densest sub-hypergraph model, and the planted multipartite hypergraph model.

Chuyang Ke, Jean Honorio

We study the problem of efficient exact partitioning of the hypergraphs generated by high-order planted models. A high-order planted model assumes some underlying cluster structures, and simulates high-order interactions by placing hyperedges among nodes. Example models include the disjoint hypercliques, the densest subhypergraphs, and the hypergraph stochastic block models. We show that exact partitioning of high-order planted models (a NP-hard problem in general) is achievable through solving a computationally efficient convex optimization problem with a tensor nuclear norm constraint. Our analysis provides the conditions for our approach to succeed on recovering the true underlying cluster structures, with high probability.

Chuyang Ke, Jean Honorio

In this paper we propose an algorithm for exact partitioning of high-order models. We define a general class of $m$-degree Homogeneous Polynomial Models, which subsumes several examples motivated from prior literature. Exact partitioning can be formulated as a tensor optimization problem. We relax this high-order combinatorial problem to a convex conic form problem. To this end, we carefully define the Carathéodory symmetric tensor cone, and show its convexity, and the convexity of its dual cone. This allows us to construct a primal-dual certificate to show that the solution of the convex relaxation is correct (equal to the unobserved true group assignment) and to analyze the statistical upper bound of exact partitioning.

Chuyang Ke, Jean Honorio

We analyze the necessary and sufficient conditions for exact inference of a latent model. In latent models, each entity is associated with a latent variable following some probability distribution. The challenging question we try to solve is: can we perform exact inference without observing the latent variables, even without knowing what the domain of the latent variables is? We show that exact inference can be achieved using a semidefinite programming (SDP) approach without knowing either the latent variables or their domain. Our analysis predicts the experimental correctness of SDP with high accuracy, showing the suitability of our focus on the Karush-Kuhn-Tucker (KKT) conditions and the spectrum of a properly defined matrix. As a byproduct of our analysis, we also provide concentration inequalities with dependence on latent variables, both for bounded moment generating functions as well as for the spectra of matrices. To the best of our knowledge, these results are novel and could be useful for many other problems.

Chuyang Ke, Jean Honorio

We analyze the information-theoretic limits for the recovery of node labels in several network models. This includes the Stochastic Block Model, the Exponential Random Graph Model, the Latent Space Model, the Directed Preferential Attachment Model, and the Directed Small-world Model. For the Stochastic Block Model, the non-recoverability condition depends on the probabilities of having edges inside a community, and between different communities. For the Latent Space Model, the non-recoverability condition depends on the dimension of the latent space, and how far and spread are the communities in the latent space. For the Directed Preferential Attachment Model and the Directed Small-world Model, the non-recoverability condition depends on the ratio between homophily and neighborhood size. We also consider dynamic versions of the Stochastic Block Model and the Latent Space Model.

Haichuan Yang, Shupeng Gui, Chuyang Ke et al.

The cardinality constraint is an intrinsic way to restrict the solution structure in many domains, for example, sparse learning, feature selection, and compressed sensing. To solve a cardinality constrained problem, the key challenge is to solve the projection onto the cardinality constraint set, which is NP-hard in general when there exist multiple overlapped cardinality constraints. In this paper, we consider the scenario where the overlapped cardinality constraints satisfy a Three-view Cardinality Structure (TVCS), which reflects the natural restriction in many applications, such as identification of gene regulatory networks and task-worker assignment problem. We cast the projection into a linear programming, and show that for TVCS, the vertex solution of this linear programming is the solution for the original projection problem. We further prove that such solution can be found with the complexity proportional to the number of variables and constraints. We finally use synthetic experiments and two interesting applications in bioinformatics and crowdsourcing to validate the proposed TVCS model and method.

Chuyang Ke, Yan Jin, Heather Evans et al.

Surgical Site Infection (SSI) is a national priority in healthcare research. Much research attention has been attracted to develop better SSI risk prediction models. However, most of the existing SSI risk prediction models are built on static risk factors such as comorbidities and operative factors. In this paper, we investigate the use of the dynamic wound data for SSI risk prediction. There have been emerging mobile health (mHealth) tools that can closely monitor the patients and generate continuous measurements of many wound-related variables and other evolving clinical variables. Since existing prediction models of SSI have quite limited capacity to utilize the evolving clinical data, we develop the corresponding solution to equip these mHealth tools with decision-making capabilities for SSI prediction with a seamless assembly of several machine learning models to tackle the analytic challenges arising from the spatial-temporal data. The basic idea is to exploit the low-rank property of the spatial-temporal data via the bilinear formulation, and further enhance it with automatic missing data imputation by the matrix completion technique. We derive efficient optimization algorithms to implement these models and demonstrate the superior performances of our new predictive model on a real-world dataset of SSI, compared to a range of state-of-the-art methods.