Tag Archives: class project

Markov assumption and regression

When doing unsupervised learning (well… it’s not entirely unsupervised but still) with sequences a possible way to map our problem to a supervised learning problem is making  the Markov assumption of order k.

To clarify, in a sequence of size T we are trying for example to maximize the likelihood \mathbb{P}(x_{1}, x_{2}, \dots, x_{T-1}, x_{T}) = \prod_{t=1}^{T}{\mathbb{P}(x_{t} \mid x_{1}, \dots, x_{t-1})}. The Markov assumption of order k is stating that \mathbb{P}(x_{t} \mid x_{t-1}, \dots, x_{t-1}) = \mathbb{P}(x_{t} \mid x_{t-k}, \dots, x_{t-1}). AR(p) is a special case (the linear one) of such model.

So we just have to define such conditional model (including the limit case for the k first step) in the same way we would define a supervised regression model, thus obtaining a probabilistic model with which we maximize likelihood.

Anyway, this is just to try to justify the name here.

P.S: There is still no preprocessing yet. I’m not using phones AND phonemes. If people want to add that, feel free to make a separate branch.

P.P.S: I’m working with Vincent for a more pylearn2-friendly implementation of this.

EDIT: Here are some occurrences of such modelization:

– First test with PyLearn2

Speech synthesis project description and first attempt at a regression MLP

Initial experiment: ’aaaaaa’ and ‘oooooo’

– FIRST EXPERIMENT — VANILLA MLP WITH THEANO

I might have forgotten some. If so please tell me.

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