Abstract: We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in R. Our study covers both the case where the true underlying density is log-concave, and where this model is misspecified. We begin by showing that for a sequence of log-concave densities, convergence in distribution implies much s...

We consider composite minimax optimization problems where the goal is to find a saddle-point of large sum non-bilinear objective functions augmented by simple regularizers for primal and dual variables. For such problems, under average-smoothness assumption, we propose accelerated stochastic variance-reduced algorithms with optimal up logarithmic factors complexity bounds. In particular, strong...

IBM Model 1 is a classical alignment model. Of the first generation word-based SMT models, it was the only such model with a concave objective function. For concave optimization problems like IBM Model 1, we have guarantees on the convergence of optimization algorithms such as Expectation Maximization (EM). However, as was pointed out recently, the objective of IBM Model 1 is not strictly conca...

Based on the convex-concave relaxation procedure (CCRP), the (extended) path following algorithms were recently proposed to approximately solve the equal-sized graph matching problem, and exhibited a state-of-the-art performance (Zaslavskiy et al., 2009; Liu et al., 2012). However, they cannot be used for subgraph matching since either their convex or concave relaxation becomes no longer applic...

BACKGROUND Efforts to select the appropriate number of implants in adolescent idiopathic scoliosis (AIS) instrumentation are hampered by a lack of biomechanical studies. The objective was to biomechanically evaluate screw density at different regions in the curve for AIS correction to test the hypothesis that alternative screw patterns do not compromise anticipated correction in AIS when using ...

IBM Model 1 is a classical alignment model. Of the first generation word-based SMT models, it was the only such model with a concave objective function. For concave optimization problems like IBM Model 1, we have guarantees on the convergence of optimization algorithms such as Expectation Maximization (EM). However, as was pointed out recently, the objective of IBM Model 1 is not strictly conca...

Concave properties play a dominate role in solving both classic and fuzzy optimization problems. However, since fuzzy problems are generally represented by sets, not crisp numbers, various aggregation schemes are needed to manipulate and to combine the different elements in a fuzzy optimization problem. Based on these different aggregations, various concavity properties can be formulated and ex...

Utility-based power control in wireless networks has been widely recognized as an effective mechanism to managing co-channel interferences. It is based on the maximization of system utility subject to power constraints, which is referred to as power control optimization problem. Global coupling between the mutual interference of wireless channels increases the difficulty of searching global opt...

We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of expectation of the supremum of “symmetric exponential” processes compared to the Gaussian ones in the Chevet inequality. This is used to give sharp upper estimate for a quantity Γk,m that controls uniformly the Euclidean operator norm of the sub-matrices ...

This paper presents a simple and effective method to fabricate a polydimethyl-siloxane (PDMS) microlens array with a high fill factor, which utilizes the UV proximity printing and photoresist replication methods. The concave microlens array mold was made using a printing gap in lithography process, which utilizes optical diffraction of UV light to deflect away from the aperture edges and produc...