Likelihood Geometry

Information Geometry and Maximum Likelihood Criteria

Dierential Geometry of Autoregressive Fractionally Integrated Moving Average Models

The di erential geometry of autoregressive fractionally integrated moving average processes is developed. Properties of Toeplitz forms associated with the spectral density functions of these long memory processes are used to compute the geometric quantities. The role of these geometric quantities on the asymptotic bias of the maximum likelihood estimates of the model parameters and on the Bartl...

Information-geometric Analysis of Iterative Receiver Structures

This thesis gives an introduction to basic concepts of information geometry, a theory that uses notions of differential geometry to describe information and probabilities. These concepts are applied to the analytic description of an iterative receiver for bit interleaved coded modulation (BICM). The operation of the receiver’s subblocks are recognized as implicit projections of input probabilit...

Information geometry of maximum partial likelihood estimation for channel equalization

Information geometry of partial likelihood is constructed and is used to derive the em-algorithm for learning parameters of a conditional distribution model through information -theoretic projections. To construct the coordinates of the information geometry, an Expectation-Maximization (EM) framework is described for the distribution learning problem using the Gaussian mixture probability model...

Randomness criteria in terms of α-divergences

Vovk’s randomness criterion characterizes sequences that are random relative to two distinct computable probability measures. The uniqueness of the criterion lies in the fact that, unlike the standard criterion based on the likelihood ratio test, it is expressed in terms of a geometrical quantity, the Hellinger distance, on the space of probability measures. In this paper, we generalize the ran...