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performed on those acoustic signals, where every 10ms (frame rate) a segment of the
acoustic signal of 64ms around a time center position was extracted. Word level tran-scriptions
were used for generating phone level time segmentations on the acoustic sig-nals
by using automatic forced Viterbi alignment techniques. Using the phone level time
segmentations, the collection of those acoustic frame vectors, dimension K = 1024,
with their corresponding phone class information (47 classes) was created, where we
considered one session of the data comprising N = 14979 supervised sample points.
Finally for creating the set of feature representations, we use the Daubechies’ maxi-mally
flat filter (db4) for the WP basis family [19, 77], and the energy on the resulting
bands. We first present some analysis of the minimum cost tree pruning in terms of
topology of those solutions (the optimal filter bank decomposition problem) and then
we evaluate performances associated with those solutions.
3.6.2 Analysis of the MI Gain and Optimal Tree Pruning
We estimated the CMI gains in (3.11), using the algorithm presented in Section 3.5. We
considered s = 8, r = 2 for generating the product refinement (associated with the MI
gain obtained by refining the product partition), following the general recommendations
suggested in [18]. We tried different configurations for and Nc, which strongly govern
the tradeoff between approximation and estimation error. We conducted an exhaustive
analysis of the CMI estimation obtained across those configurations observing marginal
discrepancies on the relative differences of CMI estimated values across scale and fre-quency
bands. In this respect, it is important to point out that the relative differences
among the CMI values
(l, j) : 8l 2 1, .., 6, j 2 0, .., 2l − 1
fully characterize the
topology of solutions of the minimum cost tree pruning problem. This behavior can
be explained because the implicit over-estimation (because of estimation error) and
under-estimation (because of quantization) uniformly affect all the CMI estimations
64
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 77 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | performed on those acoustic signals, where every 10ms (frame rate) a segment of the acoustic signal of 64ms around a time center position was extracted. Word level tran-scriptions were used for generating phone level time segmentations on the acoustic sig-nals by using automatic forced Viterbi alignment techniques. Using the phone level time segmentations, the collection of those acoustic frame vectors, dimension K = 1024, with their corresponding phone class information (47 classes) was created, where we considered one session of the data comprising N = 14979 supervised sample points. Finally for creating the set of feature representations, we use the Daubechies’ maxi-mally flat filter (db4) for the WP basis family [19, 77], and the energy on the resulting bands. We first present some analysis of the minimum cost tree pruning in terms of topology of those solutions (the optimal filter bank decomposition problem) and then we evaluate performances associated with those solutions. 3.6.2 Analysis of the MI Gain and Optimal Tree Pruning We estimated the CMI gains in (3.11), using the algorithm presented in Section 3.5. We considered s = 8, r = 2 for generating the product refinement (associated with the MI gain obtained by refining the product partition), following the general recommendations suggested in [18]. We tried different configurations for and Nc, which strongly govern the tradeoff between approximation and estimation error. We conducted an exhaustive analysis of the CMI estimation obtained across those configurations observing marginal discrepancies on the relative differences of CMI estimated values across scale and fre-quency bands. In this respect, it is important to point out that the relative differences among the CMI values (l, j) : 8l 2 1, .., 6, j 2 0, .., 2l − 1 fully characterize the topology of solutions of the minimum cost tree pruning problem. This behavior can be explained because the implicit over-estimation (because of estimation error) and under-estimation (because of quantization) uniformly affect all the CMI estimations 64 |
