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3.7 Discussion and FutureWork
It is important to remind the reader that although the presented formulation is theoreti-cally
supported by the fact that the MPE-SR needs to address a complexity regularization
problem, this optimization problem is practically intractable and requires the introduc-tion
of approximations, in particular concerning the probability of error. In this paper
empirical MI is adopted for that purpose. This choice has some theoretical justification
in terms of information theoretic inequalities and monotonic behavior of the indicator
across sequence of embedded transformation of the data [16], however tightness is not
guaranteed. In that respect the presented formulation is open to consider alternative
fidelity criteria. The empirical risk (ER) is a natural candidate with a strong theoretical
support [21, 71], however the optimization problem requires an exhaustive evaluation in
our alphabet of feature transformations, which for reasonable dimension of the problem
is impractical. Another attractive alternative is the family of Ali-Silvey distances mea-sures,
used to evaluate the effect of vector quantization in hypothesis testing problems
[54, 35], or even empirical indicators like Fisher like scatter ratios [26]. This is an inter-esting
direction for future research, where as presented in this work additivity property
of these indicators, with respect to structure of WP basis, can be studied to extend algo-rithmic
solutions, or alternatively, greedy algorithms can be proposed and empirically
evaluated, when the resulting basis selection problem does not admit polynomial time
algorithmic solutions.
Concerning the presented phone classification experiments, the proposed data-driven
feature extraction offers promising results, however a systematic study of the problem
still remains to be conducted to explore the full potentiality of the proposed formulation.
This may include a careful design of the two channel filter bank evaluating its impact in
classification performances [9], the use of other tree-structured bases families, as well
as experimental validation under more general acoustic conditions.
68
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 81 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | 3.7 Discussion and FutureWork It is important to remind the reader that although the presented formulation is theoreti-cally supported by the fact that the MPE-SR needs to address a complexity regularization problem, this optimization problem is practically intractable and requires the introduc-tion of approximations, in particular concerning the probability of error. In this paper empirical MI is adopted for that purpose. This choice has some theoretical justification in terms of information theoretic inequalities and monotonic behavior of the indicator across sequence of embedded transformation of the data [16], however tightness is not guaranteed. In that respect the presented formulation is open to consider alternative fidelity criteria. The empirical risk (ER) is a natural candidate with a strong theoretical support [21, 71], however the optimization problem requires an exhaustive evaluation in our alphabet of feature transformations, which for reasonable dimension of the problem is impractical. Another attractive alternative is the family of Ali-Silvey distances mea-sures, used to evaluate the effect of vector quantization in hypothesis testing problems [54, 35], or even empirical indicators like Fisher like scatter ratios [26]. This is an inter-esting direction for future research, where as presented in this work additivity property of these indicators, with respect to structure of WP basis, can be studied to extend algo-rithmic solutions, or alternatively, greedy algorithms can be proposed and empirically evaluated, when the resulting basis selection problem does not admit polynomial time algorithmic solutions. Concerning the presented phone classification experiments, the proposed data-driven feature extraction offers promising results, however a systematic study of the problem still remains to be conducted to explore the full potentiality of the proposed formulation. This may include a careful design of the two channel filter bank evaluating its impact in classification performances [9], the use of other tree-structured bases families, as well as experimental validation under more general acoustic conditions. 68 |
