Transcript lecture9
LING 696B: Final thoughts on nonparametric methods, Overview of speech processing 1 For those who are taking the class for credits Talk to me some time about what you are planning to do (term project / homeworks) My OH: TR 2:00-3:00 2 Review: inductive inference from last time Hypothesis Prediction Estimation Old data New data Interpolation/ Smoothing 3 Example from last time: Transductive SVM Generalization can also depend on other new data (see demo) 4 Example from last time: Gaussian process Infinite feed-forward neural net: Hidden: hj(x) = tanh(i vij xi + aj) Output: ok(x) = j wjk hj(x) + bk Weights: vij , wjk ; bias: aj , bk Don’t train the network with backprop: letting weights be random, then this network becomes a Gaussian process model Another non-parametric machine (see demo) Hidden units can be thought of as complex kernel extensions -- simple kernels work too 5 Making non-parametric method more analogy-like Function approximation: predict yY from (x1, y1), …, (xN, yN) and a new xX Building blocks of predictor: kernel functions K(x1, x2): similarity between x1 and x2 This is not yet “analogy” -- xRn has no structure (data points) 6 Making non-parametric method more analogy-like What if the input x has some structure? Example: x1, x2 are sequences Extension: choose kernel functions sensitive to the structure of x1, x2 , e.g. string kernels Kt(x1, x2) = number of common subsequences of length t Finding the “right” metric requires some understanding of the structure Example: p kernels K(x1, x2)= i p(x2|h)p(x1|h)p(h) 7 Making non-parametric method more analogy-like What if the output y has some structure? Make the error function sensitive to the structure of y (intense computations) These extensions have made the nonparametric, discriminative methods (e.g. SVM) “outperform” other ones in many tasks 8 Making non-parametric method more analogy-like What if the output has some structure? Make the error function sensitive to the structure of y (intense computations) These extensions have made the nonparametric, discriminative methods (e.g. SVM) “outperform” other ones in many tasks One exception: speech 9 Final thoughts on nonparametric models Machine: most non-parametric methods look like the following minimize (error + constant*complexity) 10 Final thoughts on nonparametric models Machine: most non-parametric methods look like the following minimize (error + constant*complexity) People: are often able to generalize without relying on explicit rules 11 Final thoughts on nonparametric models Machine: most non-parametric methods look like the following minimize (error + constant*complexity) People: are often able to generalize without relying on explicit rules Connectionist propaganda often sells this Yet unable to control either the error or complexity 12 Final thoughts on nonparametric models Why not build explicit similarity/analogy models with non-parametric methods? 13 Final thoughts on nonparametric models Why not build explicit similarity/analogy models with non-parametric methods? Term project idea: find some experimental data from literature, and build a model that “outperforms” neural nets 14 Final thoughts on nonparametric models Why not build explicit similarity/analogy models with non-parametric methods? Term project idea: find some experimental data from literature, and build a model that “outperforms” neural nets Maybe “outperform” isn’t the right goal How does the model help us understand people? 15 Moving on to phonology “these problems do not arise when phonetic transcription is understood in the terms outlined above, that is, not as a direct record of the speech signal, but rather as a representation of what the speaker of a language takes to be the phonetic properties of an utterance…” -- SPE p. 294 16 Alternative to feature/ segment representations? Exemplar people Yet convincing arguments for real alternatives are few Coleman paper: maybe should explore more “realistic” representations by looking at acoustics This is often hard, seen in many years of research on speech recognition 17 Ladefoged’s experiment “There was once a young rat named Arthur, who could never take the trouble to make up his mind. “ Superimposed with a word “dot” Where is “dot”? 18 A very quick tour of speech processing Dimension reduction: finding basis for speech signals Most often used: fourier basis (sinusoids) Orthogonal v.s. overcomplete basis Short-time processing assumption: taking snapshots over time No perfect snapshots: either loses time or frequency resolution 19 A zoo of signal representations LPC/reflection coefficients 20 A zoo of signal representations Mel-frequency filterbank / cepstra 21 A zoo of signal representations PLP/RASTA spectra/cepstra for “linguistics” 22 The perceptual relevance of distance metrics People do not information from all frequency bands to get the linguistic content Example: low-pass, high-pass and band-pass filtered speech 23 Extending distance metric to sequences Dynamic time warping Template-based method Depends on distance metric between single frames Often requires many heuristics (large literature) See example 24