We describe a method for computing provably exact maximum a posteriori (MAP) estimates for a subclass of problems on graphs with cycles. The basic idea is to represent the original problem on the graph with cycles as a convex combination of tree-structured problems. A convexity argument then guarantees that the optimal value of the original problem (i.e., the log probability of the MAP assignme...

We introduce a pathwise algorithm for the Cox proportional hazards model, regularized by convex combinations of ℓ1 and ℓ2 penalties (elastic net). Our algorithm fits via cyclical coordinate descent, and employs warm starts to find a solution along a regularization path. We demonstrate the efficacy of our algorithm on real and simulated data sets, and find considerable speedup between our algori...

In this paper, a necessary and sufficient coefficient are given for functions in a class of complex valued meromorphic harmonic univalent functions of the form f = h + ḡ using Salagean operator. Furthermore, distortion theorems, extreme points, convolution condition and convex combinations for this family of meromorphic harmonic functions are obtained. Keywords—Harmonic mappings, Meromorphic fu...

We describe a class of facets of the polytope of convex combinations of the collection of even n × n permutation matrices. As a consequence, we prove the conjecture of Brualdi and Liu [4] that the number of facets of the polytope is not bounded by a polynomial in n.

In the present paper, we consider the subclass of meromorphic univalent functions S∗ p [k, α, β, c] with fixed second positive coefficient. The object of the present paper is to show coefficient estimates, convex liner combinations, some distortion theorems, and redii of starlikeness and convexity for f(z) in the class S∗ p [k, α, β, c].

We discuss in this paper Sche e’s method for constructing simultaneous con!dence intervals which hold for all linear combinations of the parameters subject to the weight vector being restricted to a convex cone. c © 2003 Elsevier B.V. All rights reserved.

We provide a PAC-Bayesian bound for the expected loss of convex combinations of classifiers under a wide class of loss functions (which includes the exponential loss and the logistic loss). Our numerical experiments with Adaboost indicate that the proposed upper bound, computed on the training set, behaves very similarly as the true loss estimated on the testing set.

In the paper we introduce classes of functions related to a class of linear combinations of two convex functions. By using properties of multivalent prestarlike functions we obtain various inclusion relationships between defined classes of functions. Some applications of the main results are also considered. Mathematics subject classification (2010): 30C45, 30C50, 30C55.

The purpose of the present paper is to establish some results involving coefficient conditions, distortion bounds, extreme points, convolution, convex combinations and neighborhoods for a new class of harmonic univalent functions in the open unit disc. We also discuss a class preserving integral operator. Relevant connections of the results presented here with various known results are briefly ...

We show that a very simple modification of the Pure Greedy Algorithm for approximating functions by sparse sums from a dictionary in a Hilbert or more generally a Banach space has optimal convergence rates on the class of convex combinations of dictionary elements. AMS subject classification: 41A25, 41A46.