8

On that subject I recommend you to read a very good paper by James Baker and others who were actually responsible for introduction of HMM in speech: A Historical Perspective of Speech Recognition http://cacm.acm.org/magazines/2014/1/170863-a-historical-perspective-of-speech-recognition/abstract Using Markov models to represent language knowledge was ...


5

I suspect machine learning is the wrong approach. Instead, I suspect you will do better to define a metric and measure the metric, or define a hypothesis and use hypothesis testing. You are not trying to predict the future evolution of these values; that's something that ML might be suitable for, but that's not what you're trying to do, so ML doesn't seem ...


5

Ad Question 1: Assuming that your assumptions on how the catalogue is used -- that is the choice of the next cell only depends on the current (or constantly many preceeding) cell(s), not the (full) history -- then yes, you can use a Markov Chain to model it. However, you do not seem to need the "Hidden" part; this is only useful if you have (probabilistic) ...


4

It is defined to be a probability. A probability is by definition already normalized. In particular, we are guaranteed that $$\sum_{j=1}^N \gamma_j(1) = 1,$$ as there are only $N$ possibilities for the state that you're in at time $1$, and these $N$ cases have no overlap.


4

Yes. Construct the product automaton. The "product construction" is a standard construction from automata theory class (e.g., typically taught in the context of finite-state automata). It can be applied to HMM's as well, and it will do exactly what you want. For your example, the resulting HMM will have 9 states. Each state in the resulting HMM will a ...


3

I think the key is to abstract your problem by finding appropriate features. For example a feature could be the minimal distance between the two curves. Or how many times do they cross over. Or how many steps do they stay less than K units away from each other. Think about features that will capture convergence and divergence. Once you have the right ...


3

I want to build a Automatic Speech Recognition (ASR) engine for myself, but I've no idea from where to start. Start with trying existing open source speech recognition system, learn how they work, play with them. Check http://cmusphinx.sourceforge.net. I've read that most ASR's are build upon Hidden Markov Models, but also I've read that HMM is limited ...


3

Hidden Markov Models were used to model phoneme units in words for speech recognition starting in the late 1980s. an early paper cited is [9] in the following. Levinson, Ljolje, Miller, "Large vocabulary speech recognition using a hidden Markov model for acoustic/ phonetic classification" in Proc. IEEE Intl. Conf. Acoust., Speech, SIgnal Processing (New ...


3

The Viterbi algorithm solves the problem. It calculates the most probable state sequence for an HMM given an observation sequence. In your example, ring sizes are observations and temperatures are hidden states. I suggest to refer to the Wikipedia article about the Viterbi algorithm (http://en.wikipedia.org/wiki/Viterbi_algorithm). It contains an example of ...


2

Isn't this exactly the same question you asked previously? I'll make some additional comments and add some links here. Hopefully that will help. is there are any particular reason why we prefere to solve it by generative model with a lot of assumption and not directly by estimating $P(Y∣X)$, given the training corpus it's still possible to estimate $p(y_i∣...


2

A simple web search leads to a whole lecture by Christopher Lee. I did not watch it entirely, but it seems to be a slow, thorough take on the algorithm with an example walk-through on paper similar to the video you link (if longer).


2

I would just use product states/transitions and probabilities. Say accelerometer has states A, B... Say video steam has states 1, 2... Then we denote probability of transition from state 'foo' to state 'bar' while emitting character baz as P(foo,bar,baz). Introduce a new HMM with states A1, A2, B1 etc. and then combine outputs from accelerometer and ...


2

It is impossible to locate the issue for sure without inspecting the implementation and results in more detail than is ontopic here. For instance, numeric algorithms always have potential issues related to the precision of the used number format, especially when dealing with (very small) probabilities. That said, two notes. Baum-Welch does only find local ...


2

A Hidden Markov Model can be expressed as an instance of a Bayesian network of a particular form. Consequently, a HMM can be viewed as an special case or kind of Bayesian network. Bayesian networks are more general, and can express other kinds of probabilistic structures as well. All HMM's are Bayesian networks, but not all Bayesian networks are HMMs.


2

Avoiding zero probabilities You probably want to be using additive smoothing when estimating probabilities from count data. With a dictionary of 80,000 words, most of those words will be very rare: many of them might never appear anywhere in your training data, or will never appear associated with a particular part of speech. Thus, your counts for those ...


1

Wikipedia is wrong. That's not what $T_1$ stores. Rather, $T_1$ stores the likelihood of a path... namely, the likelihood of the path that has the highest likelihood. What's the likelihood of a path $\hat{X}$? It is the probability of generating the output sequence $Y$ given that you followed the path $\hat{X}$, i.e., the probability $P(Y | \hat{X})$. ...


1

Actually, there are only $459^3$ transitions, not $459^4$ transitions. That helps a lot. This is because a state is a pair $(t,u)$ where $t,u$ are tags, and a transition has the form $(t,u)\to (u,v)$. In particular, you can't have $(t,u) \to (w,x)$ where $u \ne w$ (given that the state represents the last two tags). So, there are at most $459^3$ ...


1

This isn't a hidden Markov model; this is an ordinary Markov model. Take a look at Wikipedia's article on Markov chains and specifically the notion of a steady-state distribution (or stationary distribution), or read about the subject in your favorite textbook -- there are many that cover Markov chains.


1

I'll quote from the paper "Interactive Dynamic influence diagrams" (DIDs) by Polich and Gmytrasiewicz (AAMAS 2007): A dynamic influence diagram is a computational representation of a POMDP. They continue soon afterward: DIDs perform planning using a forward exploration technique known as reachability analysis. This technique explores the possible ...


1

I think since likelihood of observation sequence was asked in the question you should use the Forward Backward probabilities. This uses a technique of dynamic programming. Reference to wiki page


1

In a Bayesian network, a variable is independent from all the variables given its Markov blanket (except of course the variables in the Markov blanket). However, the Markov blanket is not the minimal set that renders two variables independent. Also note that a variable may be independent of some variables in the Markov blanket, given another set of ...


1

Normally in speech-to-text we don't already have a perfect segmentation into words, which is why we often use the HMM to match the entire speech sentence. Also, this way the HMM can take into account probabilistic information on the distribution of word bigrams (and even trigrams). If you already have a segmentation and you are sure it is correct, then you ...


1

The maximum is over the entire expression $\pi(k-1,w,u) \cdot q(v|w,u) \cdot e(x_k|v)$, for exactly the same reason that is worrying you. Moreover, under your original interpretation, there is no reason to keep $\pi(k-1,w,u)$ for the non-optimal $w$. We are forced to store $\pi(k-1,w,u)$ for all $w$ exactly for the reason you mention.


1

You can directly estimate $p(y|x)$, this is what you're doing when using a Conditional Random Fields (CRF) for tagging. As someone else said, this is called a discriminative model. A major advantage of discriminative models for tagging is they allow one to easily incorporate arbitrary features (starts with a capital letter, contains a number, contains ...


1

Answer 1 You can try to directly fit the function $\Pr[y | x]$. This is called a discriminative classification. This is typically solved via some regression mechanism such as ordinary least squares, or lasso, or ridge depending on certain assumptions of the model. Answer 2 The reason we want to factor $\Pr[x, y] = \Pr[x | y] \Pr[y]$ is because we are ...


1

From my comment: This answer on crossvalidate.SE may be of use. I wasn't aware of viterbi-training. I have only used BW or other EM-based methods in the past. Based on the answer in the link, I think BW would be the most useful. It seems Viterbi-Training gives no guarantee on bounds. However, the latter does have useful application if BW takes far too long ...


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