J. K. Freericks1,*, H. R. Krishnamurthy1,2,3, Yizhi Ge1, A. Y. Liu1, and Th. Pruschke4 1 Department of Physics, Georgetown University, Washington, DC 20057 USA 2 Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India 3 Condensed Matter Theory Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India 4 Institu...

The size |Y | of the output space Y is exponential and optimization over the entire space Y is computationally expensive. Hence in the sequential dual optimization method, the optimization of (A.6) is restricted to the set Yi = {y : αiy > 0} maintained for each example. For clarity, we present the sequential dual optimization method to solve (A.2) in Algorithm 3. The algorithm starts with Yi = ...

Let Z1, ..., Zn be i.i.d observations, where Zi = Xi +Yi and Xi and Yi are independent random variables. Assume that the distribution of Y ’s is known. The ordinary deconvolution problem is the problem of estimating the destribution of a random variables Xi from the observations Zi. In some situations (for instance, in signal processing) we don’t know the distribution of Yi but rather can assum...

Yi i.i.d. ∼ pθ∗ , i = {1, . . . , n} where θ∗ ∈ Θ. We can view pθ∗ as a member of a parametric class of distributions, P = {pθ}θ∈Θ. Our goal is to use the observations {Yi} to select an appropriate distribution (e.g., model) from P. We would like the selected distribution to be close to pθ in some sense. We use the negative log-likelihood loss function, defined as l(θ, Yi) = − log pθ(Yi). The e...

The breast can be diffusely affected by a variety of specifi c and unique disorders, including benign disorders that are closely related to physiologic changes and infl ammatory and infectious diseases, as well as by benign and malignant tumors. The clinical manifestations include unilateral or bilateral breast enlargement with/without a palpable masses, shrinkage and breast asymmetry. Thus, kn...