The mathematics of language learning

Over the past decade, attention has gradually shifted from the estimation of parameters to the learning of linguistic structure (for a survey see Smith 2011). The Mathematics of Language (MOL) SIG put together this tutorial, composed of three lectures, to highlight some alternative learning paradigms in speech, syntax, and semantics in the hopes of accelerating this trend. Compounding the enormous variety of formal models one may consider is the bewildering range of ML techniques one may bring to bear. In addition to the surprisingly useful classical techniques inherited from multivariate statistics such as Principal Component Analysis (PCA, Pearson 1901) and Linear Discriminant Analysis (LDA, Fisher 1936), computational linguists have experimented with a broad range of neural net, nearest neighbor, maxent, genetic/evolutionary, decision tree, max margin, boost, simulated annealing, and graphical model learners. While many of these learners became standard in various domains of ML, within CL the basic HMM approach proved surprisingly resilient, and it is only very recently that deep learning techniques from neural computing are becoming competitive not just in speech, but also in OCR, paraphrase, sentiment analysis, parsing and vector-based semantic representations. The first lecture will provide a mathematical introduction to some of the fundamental techniques that lie beneath these linguistic applications of neural networks, such as: BFGS optimization, finite difference approximations of Hessians and Hessianfree optimization, contrastive divergence and variational inference. Lecture 1: The mathematics of neural computing – Penn Recent results in acoustic modeling, OCR, paraphrase, sentiment analysis, parsing and vectorbased semantic representations have shown that natural language processing, like so many other corners of artificial intelligence, needs to pay more attention to neural computing. I Gaussian Mixture Models • Lagrange’s theorem • Stochastic gradient descent • typical acoustic models using GMMs and

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