A decision-directed detection scheme for multiple hypotheses is developed and analyzed. It is assumed that the probability density functions \{f_{i}(x)\} under each of the m+1 hypotheses are known, and the prior probablities \{\pi_{i}\} are unknown and sequentially estimated on the basis of previous decisions. Using a set of nonlinear transformations of the data and applying results from the stochastic approximation theory, improved algorithms are given for achieving asymptotically unbiased estimates and accelerated convergence to the true priors.

An improved decision-directed detector (Corresp.)

A decision-directed learning strategy is presented to recursively estimate (i.e., track) the time-varying a priori distribution for a multivariate empirical Bayes adaptive classification rule. The problem is formulated by modeling the prior distribution as a finite-state vector Markov chain and using past decisions to estimate the time evolution of the state of this chain. The solution is obtained by implementing an exact recursive nonlinear estimator for the rate vector of a multivariate discrete-time point process representing the decisions. This estimator obtains the Doob decomposition of the decision process with respect to the a-field generated by all past decisions and corresponds to the nonlinear least squares estimate of the prior distribution. Monte Carlo simulation results are provided to assess the performance of the estimator.

/pdf/decision-directed-multivariate-empirical-bayes-52wyvvti0k.pdf

Decision-Directed Multivariate Empirical Bayes Classification with Nonstationary Priors

Computational constraints often limit the practical applicability of coherent Bayes solutions to unsupervised sequential learning problems. These problems arise when attemps are made to learn about parameters on the basis of unclassified observations., each stemming from any one of k cases (k = 2).
In this paper, the difficulties of the Bayes process will be discussed and existing approximate learning procedures will be reviewed for broad types of problems involving mixtures of probability density. In particular a quasi-Bayes approximate learning procedure will be motivated and defined and its convergence properties will be reported for several special cases

Approximations of unsupervised Bayes learning procedures

A robust method of spectral estimation is examined which uses a decision-directed empirical Bayes receiver to estimate the time-varying a priori probability of signal occurrence in a given bin of the FFT of a signal. The a priori probability of spectral content for each bin is modeled as a finite-state Markov chain and an exact, recursive, nonlinear least squares estimator is employed to estimate the current state of the Markov process, and consequently the marginal probability for each of the bins. A generalized Bayes likelihood ratio test (GLRT) is used as the detector which feeds decisions to the state estimator. The estimate of the states is used along with a Markov probability vector to generate estimates of the a priori probability for use in the GLRT. Receiver operating characteristic curves are generated to illustrate algorithm performance.

A novel approach to time-varying spectral probability estimation

A decision-directed approach is presented for analyzing linear systems with unknown jump inputs. The system model parameters are estimated using a Kalman filter, and an empirical Bayes detection procedure is introduced to set the detector parameters, resulting in a decision-directed generalized likelihood ratio test coupled with recursive system parameter estimation. Monte Carlo results are presented to validate the performance of the algorithm.

/pdf/simultaneous-system-identification-and-decision-directed-yo787tufym.pdf

Simultaneous system identification and decision-directed detection and estimation of jump inputs to linear systems

By simple modifications of a decision-directed learning procedure, the regression curves of multidimensional stochastic approximation can be rotated further apart, leading to enhanced convergence properties. Results of a Monte Carlo simulation for a binary hypotheses testing problem are given which illustrates this faster convergence.

Modified stochastic approximation to enhance unsupervised learning

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

A. Katopis

Author Tools

Chat about Author

Papers

Modified stochastic approximation to enhance unsupervised learning