We immediately notice the similarity between the empirical risk we had seen before and the negative loglikelihood. We will see that we can regard maximum likelihood estimation as our familiar minimal empirical risk when the loss function is chosen appropriately. In the meantime note that minimizing (1) yields our familiar square-error loss if Wi’s are Gaussian. If the Wi’s are Laplacian (pW (w)...

We describe a method for Maximum Likelihood (ML) parameter estimation corrupted by additive white Gaussian noise. The ML cost function is maximized over the constraint that the detected data vector lie on the sphere. The results are compared with MMSE and with [2]. Simulations results shows superior performance of our method comparing to both the methods.

This correspondence investigates convexity properties of error probability in the detection of binary-valued scalar signals corrupted by additive noise. It is shown that the error probability of the maximumlikelihood receiver is a convex function of the signal power when the noise has a unimodal distribution. Based on this property, results on the optimal time-sharing strategies of transmitters...

We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-exponential kernels. Hyperparameter learning in this model can be seen as Bayesia...

An integer additive set-indexer is defined as an injective function f : V (G) → 2N0 such that the induced function gf : E(G) → 2N0 defined by gf (uv) = f(u) + f(v) is also injective, where f(u) + f(v) is the sumset of f(u) and f(v). If gf (uv) = k ∀ uv ∈ E(G), then f is said to be a k-uniform integer additive set-indexers. An integer additive set-indexer f is said to be a weak integer additive ...

High dimensional nonparametric regression is an inherently difficult problem with known lower bounds depending exponentially in dimension. A popular strategy to alleviate this curse of dimensionality has been to use additive models of first order, which model the regression function as a sum of independent functions on each dimension. Though useful in controlling the variance of the estimate, s...

The problem of rationally engineering protein molecules can be simplified where effects of mutations on protein function are additive. Crystal structures of single and double mutants in the hydrophobic core of gene V protein indicate that structural and functional effects of core mutations are additive when the regions structurally influenced by the mutations do not substantially overlap. These...

In commonly used functional regression models, the regression of a scalar or functional response on the functional predictor is assumed to be linear. This means the response is a linear function of the functional principal component scores of the predictor process. We relax the linearity assumption and propose to replace it by an additive structure. This leads to a more widely applicable and mu...