Preparation First, based on the definitions of A t , Y t , ˜ Z t and Z t , we can write g t = G(s t , r t , X t) = p −1 st p −1 rt (I − X t X ⊤ t)(E st ⊙ A)(E ·rt ⊙ X) = (I − X t X ⊤ t)A t Y t. Then from (6), we have X t+1 = X t + α t g t W t − α 2 t 2 X t g ⊤ t g t W t. Since W t = (I + α 2 t 4 g ⊤ t g t) −1 = I − α 2 t 4 g ⊤ t g t + O(α 4 t), we get X t+1 = X t + α t A t Y t − α t X t X ⊤ t A...

1 Data Sources • Amazon abbreviates the AmazonBinary dataset in Chen’s collection. • Iris is from the UCI machine learning repository . • Votes is from the UCI machine learning repository . • ORL is from the Database of Faces of AT&T. • PIE is from CMU/VASC Image Database. • YaleB is from the Extended Yale Face Database B. • COIL20 is from Columbia University Image Library. • Isolet is from the...

A distributed Nash equilibrium seeking algorithm is presented for networked games. We assume an incomplete information available to each player about the other players’ actions. The players communicate over a strongly connected digraph to send/receive the estimates of the other players’ actions to/from the other local players according to a gossip communication protocol. Due to asymmetric infor...

Standard credit risk models rely on a doubly stochastic structure. Conditional on the evolution of common factors, defaults are independent. Recently, tests by Das, Duffie, Kapadia and Saita (2007) have cast doubt on the empirical validity of this assumption. We modify their estimation approach in two ways. First, we model intra-month patterns in observed defaults. Second, we estimate default i...

Establishing correspondence between features in two images of the same scene taken from different viewing angles is a challenging problem in image processing and computer vision. However, its solution is an important step in many applications like wide baseline stereo, 3D model alignment, creation of panoramic views etc.In this paper, we propose a technique for registration of two images of a f...

A formula for Glynn’s hyperdeterminant detp (p prime) of a square matrix shows that the number of ways to decompose any integral doubly stochastic matrix with row and column sums p− 1 into p− 1 permutation matrices with even product, minus the number of ways with odd product, is 1 (mod p). It follows that the number of even Latin squares of order p− 1 is not equal to the number of odd Latin squ...

In this paper we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between L2ρ(R ;R)⊗Lρ(R ;R) valued solutions of backward doubly stochastic differential equations (BDSDEs) on infinite horizon and the stationary solutions of the SPDEs. Moreover, we prove the existence and uniqueness of the solutions of BDSDEs on both finite ...

A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When points reside Euclidean space, a widespread approach to form by Gaussian kernel with pairwise distances, and follow certain normalization (e.g., row-stochastic or its symmetric variant). We demonstrate that doubly stochastic zero main diagonal (i.e., no...

Let {Xk, k ≥ 1} be a sequence of independent, identically distributed nonnegative random variables with common distribution function F and finite expectation μ > 0. Under the assumption that the tail probability F(x) = 1−F(x) is consistently varying as x tends to infinity, this paper investigates precise large deviations for both the partial sums Sn and the random sums SN(t), where N(·) is a co...