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Figure 5.3: Empirical mutual information trajectories for different estimation tech-niques.
ML: maximum likelihood plug-in estimate under Gaussian parametric assump-tion,
TSVQ: tree-structured data-depenednt partition, GESS: Gessaman’s statistically
equivalent blocks, kernel: kernel plug-in estimate and PR-class: product classical
histogram-based estimate. Performances are reported for one realization of the empir-ical
process across sampling lengths in the log-scale. Data simulated with correlation
coefficient r = 0.3.
These results show that under different levels of statistical dependency between X and
Y our data-driven non-product histogram-based constructions (Gessaman and TSVQ)
present performance improvements compared to the two classical techniques, in terms
of both the bias and standard deviations. These performance values were computed from
1000 independent realizations of the empirical process. In particular, the bias differences
are substantial in the small sample regime [1 − 104], with respect to classical product
histogram approaches, supporting the conjecture that motivated this work, claiming that
data-dependent partitions can improve the performance of classical product histogram
based constructions in the small sample regime. These techniques also perform better
than the kernel plug-in estimate, particularly clear in the sampling range [1 − 102] and
across all correlation scenarios. A similar performance trend was also observed in [78].
Figures 5.3 and 5.4 show the characteristic behavior of the estimates for a realization of
the empirical process, and two correlation scenarios r = 0.3 and r = 0.8 respectively.
161
Object Description
| Title | On optimal signal representation for statistical learning and pattern recognition |
| Author | Silva, Jorge |
| Author email | jorgesil@usc.edu; josilva@ing.uchile.cl |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Electrical Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2008-06-23 |
| Date submitted | 2008 |
| Restricted until | Unrestricted |
| Date published | 2008-10-21 |
| Advisor (committee chair) | Narayanan, Shrikanth S. |
| Advisor (committee member) |
Kuo, C.-C. Jay Ordóñez, Fernando I. |
| Abstract | This work presents contributions on two important aspects of the role of signal representation in statistical learning problems, in the context of deriving new methodologies and representations for speech recognition and the estimation of information theoretic quantities.; The first topic focuses on the problem of optimal filter bank selection using Wavelet Packets (WPs) for speech recognition applications. We propose new results to show an estimation-approximation error tradeoff across sequence of embedded representations. These results were used to formulate the minimum probability of error signal representation (MPE-SR) problem as a complexity regularization criterion. Restricting this criterion to the filter bank selection, algorithmic solutions are provided by exploring the dyadic tree-structure of WPs. These solutions are stipulated in terms of a set of conditional independent assumptions for the acoustic observation process, in particular, a Markov tree property across the indexed structure of WPs. In the technical side, this work presents contributions on the extension of minimum cost tree pruning algorithms and their properties to affine tree functionals. For the experimental validation, a phone classification task ratifies the goodness of Wavelet Packets as an analysis scheme for non-stationary time-series processes, and the effectiveness of the MPE-SR to provide cost effective discriminative filter bank solution for pattern recognition.; The second topic addresses the problem of data-dependent partitions for the estimation of mutual information and Kullback-Leibler divergence (KLD). This work proposes general histogram-based estimates considering non-product data-driven partition schemes. The main contribution is the stipulation of sufficient conditions to make these histogram-based constructions strongly consistent for both problems. The sufficient conditions consider combinatorial complexity indicator for partition families and the use of large deviation type of inequalities (Vapnik-Chervonenkis inequalities). On the application side, two emblematic data-dependent constructions are derived from this result, one based on statistically equivalent blocks and the other, on a tree-structured vector quantization scheme. A range of design values was stipulated to guarantee strongly consistency estimates for both framework. Furthermore, experimental results under controlled settings demonstrate the superiority of these data-driven techniques in terms of a bias-variance analysis when compared to conventional product histogram-based and kernel plug-in estimates. |
| Keyword | signal representation in statistical learning; Bayes decision theory; basis selection; tree-structured bases and Wavelet packet (WP); complexity regularization; minimum cost tree pruning; family pruning problem; mutual information estimation; divergence estimation; data-dependent partitions; statistical learning theory; concentration inequalities; tree-structured vector quantization. |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m1684 |
| Contributing entity | University of Southern California |
| Rights | Silva, Jorge |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-Silva-2450 |
| Archival file | uscthesesreloadpub_Volume32/etd-Silva-2450.pdf |
Description
| Title | Page 174 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | Figure 5.3: Empirical mutual information trajectories for different estimation tech-niques. ML: maximum likelihood plug-in estimate under Gaussian parametric assump-tion, TSVQ: tree-structured data-depenednt partition, GESS: Gessaman’s statistically equivalent blocks, kernel: kernel plug-in estimate and PR-class: product classical histogram-based estimate. Performances are reported for one realization of the empir-ical process across sampling lengths in the log-scale. Data simulated with correlation coefficient r = 0.3. These results show that under different levels of statistical dependency between X and Y our data-driven non-product histogram-based constructions (Gessaman and TSVQ) present performance improvements compared to the two classical techniques, in terms of both the bias and standard deviations. These performance values were computed from 1000 independent realizations of the empirical process. In particular, the bias differences are substantial in the small sample regime [1 − 104], with respect to classical product histogram approaches, supporting the conjecture that motivated this work, claiming that data-dependent partitions can improve the performance of classical product histogram based constructions in the small sample regime. These techniques also perform better than the kernel plug-in estimate, particularly clear in the sampling range [1 − 102] and across all correlation scenarios. A similar performance trend was also observed in [78]. Figures 5.3 and 5.4 show the characteristic behavior of the estimates for a realization of the empirical process, and two correlation scenarios r = 0.3 and r = 0.8 respectively. 161 |
