Efficient unimodality test in clustering by signature testing

This paper provides a new unimodality test with application in hierarchical clustering methods. The proposed method denoted by signature test (Sigtest), transforms the data based on its statistics. The transformed data has much smaller variation compared to the original data and can be evaluated in a simple proposed unimodality test. Compared with the existing unimodality tests, Sigtest is more accurate in detecting the overlapped clusters and has a much less computational complexity. Simulation results demonstrate the efficiency of this statistic test for both real and synthetic data sets

Relative Entropy (RE) Based LTI System Modeling Equipped with time delay Estimation and Online Modeling

This paper proposes an impulse response modeling in presence of input and noisy output of a linear time-invariant (LTI) system. The approach utilizes Relative Entropy (RE) to choose the optimum impulse response estimate, optimum time delay and optimum impulse response length. The desired RE is the Kulback-Lielber divergence of the estimated distribution from its unknown true distribution. A unique probabilistic validation approach estimates the desired relative entropy and minimizes this criterion to provide the impulse response estimate. Classical methods have approached this system modeling problem from two separate angles for the time delay estimation and for the order selection. Time delay methods focus on time delay estimate minimizing various proposed criteria, while the existing order selection approaches choose the optimum impulse response length based on their proposed criteria. The strength of the proposed RE based method is in using the RE based criterion to estimate both the time delay and impulse response length simultaneously. In addition, estimation of the noise variance, when the Signal to Noise Ratio (SNR) is unknown is also concurrent and is based on optimizing the same RE based criterion. The RE based approach is also extended for online impulse response estimations. The online method reduces the model estimation computational complexity upon the arrival of a new sample. The introduced efficient stopping criteria for this online approaches is extremely valuable in practical applications. Simulation results illustrate precision and efficiency of the proposed method compared to the conventional time delay or order selection approaches.Comment: 13 pages, 11 figure

Learnability, Sample Complexity, and Hypothesis Class Complexity for Regression Models

The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially different complexities. Linear regression modeling is an important category of learning algorithms. The practical uncertainty of the target samples affects the generalization performance of the learned model. Failing to choose a proper model or hypothesis class can lead to serious issues such as underfitting or overfitting. These issues have been addressed by alternating cost functions or by utilizing cross-validation methods. These approaches can introduce new hyperparameters with their own new challenges and uncertainties or increase the computational complexity of the learning algorithm. On the other hand, the theory of probably approximately correct (PAC) aims at defining learnability based on probabilistic settings. Despite its theoretical value, PAC does not address practical learning issues on many occasions. This work is inspired by the foundation of PAC and is motivated by the existing regression learning issues. The proposed approach, denoted by epsilon-Confidence Approximately Correct (epsilon CoAC), utilizes Kullback Leibler divergence (relative entropy) and proposes a new related typical set in the set of hyperparameters to tackle the learnability issue. Moreover, it enables the learner to compare hypothesis classes of different complexity orders and choose among them the optimum with the minimum epsilon in the epsilon CoAC framework. Not only the epsilon CoAC learnability overcomes the issues of overfitting and underfitting, but it also shows advantages and superiority over the well known cross-validation method in the sense of time consumption as well as in the sense of accuracy.Comment: 14 pages,10 figure

Techniques for enhancing the performance of communication systems employing spread-response precoding

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (p. 65-66).by Soosan Beheshti.M.S

Minimum description complexity

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (p. 136-140).The classical problem of model selection among parametric model sets is considered. The goal is to choose a model set which best represents observed data. The critical task is the choice of a criterion for model set comparison. Pioneer information theoretic based approaches to this problem are Akaike information criterion (AIC) and different forms of minimum description length (MDL). The prior assumption in these methods is that the unknown true model is a member of all the competing sets. We introduce a new method of model selection: minimum description complexity (MDC). The approach is motivated by the Kullback-Leibler information distance. The method suggests choosing the model set for which the model set relative entropy is minimum. We provide a probabilistic method of MDC estimation for a class of parametric model sets. In this calculation the key factor is our prior assumption: unlike the existing methods, no assumption of the true model being a member of the competing model sets is needed. The main strength of the MDC calculation is in its method of extracting information from the observed data.(cont.) Interesting results exhibit the advantages of MDC over MDL and AIC both theoretically and practically. It is illustrated that, under particular conditions, AIC is a special case of MDC. Application of MDC in system identification and signal denoising is investigated. The proposed method answers the challenging question of quality evaluation in identification of stable LTI systems under a fair prior assumption on the unmodeled dynamics. MDC also provides a new solution to a class of denoising problems. We elaborate the theoretical superiority of MDC over the existing thresholding denoising methods.by Soosan Beheshti.Ph.D