Maximum Likelihood Estimation Framework Research Articles

Unsupervised visual learning of three-dimensional objects using a modular network architecture

This paper presents a modular network architecture that learns to cluster multiple views of multiple three-dimensional (3D) objects. The proposed network model is based on a mixture of non-linear autoencoders, which compete to encode multiple views of each 3D object. The main advantage of using a mixture of autoencoders is that it can capture multiple non-linear sub-spaces, rather than multiple centers for describing complex shapes of the view distributions. The unsupervised training algorithm is formulated within a maximum-likelihood estimation framework. The performance of the modular network model is evaluated through experiments using synthetic 3D wire-frame objects and gray-level images of real 3D objects. It is shown that the performance of the modular network model is superior to the performance of the conventional clustering algorithms, such as the K-means algorithm and the Gaussian mixture model.

He came, he saw, (and) he waited: an empirical analysis of inertia in technology adoption

The innovation adoption literature has focused primarily on a producer's decision of whether and how much to adopt. An equally pertinent question is when to adopt, because in the case of new technologies it often ‘pays to wait’ for more information. We propose a double-limit hurdle model to analyse adoption intensity and inertia in the context of a divisible technology. The proposed framework incorporates probit or Tobit models as testable special cases. A maximum likelihood estimation framework is set out and generalized to account for heteroscedastic errors. The empirical analysis, which uses household-level data from India's semi-arid tropics, provides new insights into the factors influencing adoption inertia and intensity.

Probabilistic visual learning for object representation

We present an unsupervised technique for visual learning, which is based on density estimation in high-dimensional spaces using an eigenspace decomposition. Two types of density estimates are derived for modeling the training data: a multivariate Gaussian (for unimodal distributions) and a mixture-of-Gaussians model (for multimodal distributions). Those probability densities are then used to formulate a maximum-likelihood estimation framework for visual search and target detection for automatic object recognition and coding. Our learning technique is applied to the probabilistic visual modeling, detection, recognition, and coding of human faces and nonrigid objects, such as hands.

A stochastic multidimensional unfolding approach for representing phased decision outcomes

This paper presents a stochastic multidimensional unfolding (MDU) procedure to spatially represent individual differences in phased or sequential decision processes. The specific application or scenario to be discussed involves the area of consumer psychology where consumers form judgments sequentially in their awareness, consideration, and choice set compositions in a phased or sequential manner as more information about the alternative brands in a designated product/service class are collected. A brief review of the consumer psychology literature on these nested congnitive sets as stages in phased decision making is provided. The technical details of the proposed model, maximum likelihood estimation framework, and algorithm are then discussed. A small scale Monte Carlo analysis is presented to demonstrate estimation proficiency and the appropriateness of the proposed model selection heuristic. An application of the methodology to capture awareness, consideration, and choice sets in graduate school applicants is presented. Finally, directions for future research and other potential applications are given.

Exact maximum likelihood parameter estimation of superimposed exponential signals in noise

A unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise, encompassing both the time series and the array problems, is presented. An exact expression for the ML criterion is derived in terms of the linear prediction polynomial of the signal, and an iterative algorithm for the maximization of this criterion is presented. The algorithm is equally applicable in the case of signal coherence in the array problem. Simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques. The algorithm is similar to those independently derived by Kumaresan et al. In addition to its practical value, the present formulation is used to interpret previous methods such as Prony's, Pisarenko's, and modifications thereof.

Multiple-Window Parallel Adaptive Boundary Finding in Computer Vision

The problem considered in this paper is the estimation of highly variable object boundaries in noisy images. Boundaries may be those of a tank in an IR image, a spinal canal in a CAT scan, a cloud in a visible light image, etc. Or they may be internal to an object such as the boundary between a spherical surface and a cylindrical surface in a manufactured object. The focus of the paper is on parallel multiple-window boundary estimation algorithms. Here the image field is parti-tioned into an array of rectangular windows, and boundary finders are run simultaneously within the windows. The boundary segments found within the windows are then seamed together to obtain meaningful global boundaries. The entire procedure is treated within a maximum likelihood estimation framework that we have developed for boundary finding. Although our multiple-window estimation approach can be used with a number of local boundary finding algorithms, we concen-trate on one which is based on dynamic programming and will produce the true maximum likelihood boundary. Some theoretical considera-tions for boundary model design and boundary-finding runtime are covered. Included is the use of a low computational cost F-test for test-ing whether a window contains a boundary, and an analytical treatment which shows that use of coarse pixels with a chi-square test or an F-test improves the probability of correctly recognizing whether a boundary is present in a window.

A likelihood approach to character weighting and what it tells us about parsimony and compatibility

The statistical framework of maximum likelihood estimation is used to examine character weighting in inferring phylogenies. A simple probabilistic model of evolution is used, in which each character evolves independently among two states, and different lineages evolve independently. When different characters have different known probabilities of change, all sufficiently small, the proper maximum likelihood method of estimating phylogenies is a weighted parsimony method in which the weights are logarithmically related to the rates of change. When rates of change are taken extremely small, the weights become more equal and unweighted parsimony methods are obtained. When it is known that a few characters have very high rates of change and the rest very low rates, but it is not known which characters are the ones having the high rates, the maximum likelihood criterion supports use of compatibility methods. By varying the fraction of characters believed to have high rates of change one obtains a ‘threshold method’ whose behavior depends on the value of a parameter. By altering this parameter the method changes smoothly from being a parsimony method to being a compatibility method. This provides us with a spectrum of intermediates between these methods. These intermediate methods may be of use in analysing real data.