Expectation Maximization

A chilly mass of air breezes against the face. Withered leaves, in colors of red, brown and yellow gather near the feet. The skies take the hue of teal blue, with a sparse scattering of clouds. Something musters in the air. A change. A transition. The coming of a new season, the making of a quiet, quantum jump. The magical phenomenon of metamorphosis – the development of that which is intricate from that which is next to nothing. The nurture of something organic, the crystallization of a set of ideas. Each day takes it a step further, and by so doing breathing into it new life. Inspiring traction, leading a steady and irreversible gain in momentum.

Much has been done, but much more remains to be done. There are many to thank, without whose raw love and sturdy support nothing could come to pass. It is a moral imperative to preserve the perspective and sharpen the focus. The entropy of strong, concerted action must be maintained and balanced with great care. Steadfast discipline and renewed devotion should and must be the forte, for nothing can be done without them.

The past semester has been exhilarating, thought-provoking and inspiring. In this place called MIT which I have come to love, I have seen some remarkable things. I’ve witnessed first-hand the power and beauty of the human mind. I’ve seen brilliance, and felt an ambiance of  possibility. It is an inexcusable blunder to let oneself be carried away by this magnificent atmosphere at the cost of one’s own health, as I have done this past semester. Yes, I’ve stumbled. But I am glad to have stumbled, for I have learned to appreciate the power of balance and proportion even better.

The magic of Hidden Markov Models

My current research involves a lot of  hidden markov modeling. Sometimes, I look at hidden markov models and think about what a gift to humanity they really are. Used in seemingly disparate areas from protein modeling to gesture & speech recognition to natural language processing, HMMs are a most fascinating set of methods. The art of observing output as dependent on a set of hidden states, and for those hidden states to emerge and to be harnessed, is simply breathtaking.

I’ve always thought of fundamental particle physics to be the most beautiful pieces of mathematical work, and have always resented not having pursued it. Hidden markov models, while paling in comparison, are still stunningly pretty. I’ve felt a strong fondness for it. There are probably even more gorgeous things out there – I can only hope that stumble upon them as a function of my research.

It’s particularly thrilling to see those hidden states to be harnessed for something that actually helps people, as I hope the case with my current work will turn out to be. For now though, I am going to be treating myself to watch and enjoy it. 🙂

Iterations and malleability

If everything could be mustered in a single pass, that would certainly be wonderful. The fact remains though, that most things are not achievable in a single pass, sometimes not even in a few passes. No matter what one’s goals are or how tough one’s predicaments may be, one has an obligation to press on with resolve and to keep trying. Repeatedly and consistently. There is no power like that of a strong will, and there are few things that cannot be done with perseverance. Concerted action renders things malleable, affording you the power to bend them at your will.

Granted, not all the variables are under your control. But certain variables are, perhaps the most important being the ability to control how they shape one’s thinking. And that is all that matters for most things.

Expectation Maximization

Just they are used to solve certain kinds of hidden markov model problems, the method of expectation maximization is a profound metaphor for all that is yet to come and how we should be leading our lives. Iterative by its very nature, it works consistently and repeatedly to unravel the hidden states that lie within.

As goals are laid and dreams created, there are many beautiful hidden things that are yet to come.

 

 

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