We analyze a maximum likelihood approach for combining phylogenetic trees into a larger "supertree." This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description (as a median tree, minimizing a weighted sum of distances to the input trees). We show that this approach to ML supertree reconstruction is statistically co...

where p above is the density function if X is continuous and the mass function if X is discrete. The MLE is denoted θ̂ or θ̂n if we wish to emphasize the sample size. Above, we suppress the dependency of L on X1, . . . , X (n) to emphasize that we are treating the likelihood as a function of θ. Note that both X and θ may be scalars or vectors (not necessarily of the same dimension) and that L may...

Many visual matching algorithms can be described in terms of the features and the inter-feature distance or metric. The most commonly used metric is the sum of squared differences (SSD), which is valid from a maximum likelihood perspective when the real noise distribution is Gaussian. However, we have found experimentally that the Gaussian noise distribution assumption is often invalid. This im...

This paper addresses the problem of autocalibration, which is a critical step in existing uncalibrated structure from motion algorithms that utilize an initialization to avoid the local minima in metric bundle adjustment. Currently, all known direct (not non-linear) solutions to the uncalibrated structure from motion problem solve for a projective reconstruction that is related to metric by som...

The majority of the approaches to the automatic recovery of a panoramic image from a set of partial views are suboptimal in the sense that the input images are aligned, or registered, pair by pair, e.g., consecutive frames of a video clip. These approaches lead to propagation errors that may be very severe, particularly when dealing with videos that show the same region at disjoint time interva...

This paper deals with the source separation problem which consists in the separation of a mixture of independent sources without a priori knowledge on the mixing matrix. When the source distributions are known in advance, this problem can be solved via the Maximum Likelihood (ML) approach by maximizing the data likelihood function using (i) the Expectation-Maximization (EM) algorithm and (ii) a...

Maximum likelihood is by far the most popular general method of estimation. Its widespread acceptance is seen on the one hand in the very large body of research dealing with its theoretical properties, and on the other in the almost unlimited list of applications. To give a reasonably general definition of maximum likelihood estimates, let X = (X1, . . . , Xn) be a random vector of observations...

We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML has appealing theoretical properties, but is difficult to compute exactly. Inspired by observations gleaned from exactly solvable cases, we look for an appro...

In this paper, we report on the impact that slight changes in question format have on student response to onedimensional vector subtraction tasks. We use Maximum Likelihood Estimation (MLE) analysis to analyze students’ responses on six very similar questions which vary in context (physics or mathematics), vector alignment (both pointing to the right or opposed), and operation (left-right subtr...