Location: CSE building (EBU3B) room 4140
Time: 12:30 – 1:30pm, Thursday, April 16
Host: Yoav Freund

Learning boundary detection by minimizing image segmentation error

Sebastian Seung
Howard Hughes Medical Institute and MIT

The problem of boundary detection has a long history in computer vision. In the classical approach, thresholded gradient filters were used to detect boundaries. Later on, the output of gradient filtering was “cleaned up” by incorporating contextual information through relaxation labeling, Markov random fields, graph partitioning, and other formalisms. More recently, there has been a revival of interest in using machine learning to improve accuracy by training a computer to emulate human boundary judgments. In the standard approach, a boundary detector is trained by minimizing its pixel-level disagreement with humans. However, this criterion is not appropriate if boundary detection is only a means to the ultimate goal of image segmentation, rather than an end in itself. We have invented new methods for training boundary detectors that specifically target errors with topological consequences, and do not require the computer to slavishly imitate human placement of boundaries. I will demonstrate our methods with a challenging application, tracing the branches of neurons in 3d images of brain tissue taken by electron microscopy. The empirical results show a dramatic reduction in the number of split and merge errors.

Imagine you were in a casino with a wall of slot machines, and you thought each machine has different probabilities of winning, but you dont know which one is the good one. What is the best thing to do, assuming your goal is to find the best machine, and then play it to win the most money?

You probably would play a mix of machines, and then settle on one to play. You could play each machine randomly and uniformly (i.e. roll a die, and if you roll a 6, play machine 6). This would give you a certain return. But if somehow you could know which machine was the best one, you could make more money playing that one. This dillema is known as exploration(try them all) vs exploitation(play the best one).

Formal analysis of this problem calls it the “multi-arm bandit,” (because a slot machine is sometimes called a one-arm bandit), and is a focus of a lot of current research in machine learning : a very similar problem is choosing which keywords to advertise for google ads, for example: you want to post the best ads, but also try a bunch of words, maybe you can find inexpensive keywords which generate the most clicks, and I’ve seen some talks by folks from Yahoo! research about this recently (they seem to be a little less secretive than the big G).

Or we might have the same situation in dating. You can’t date everyone, but you need to find someone to marry (if you are the marrying type). You might find someone early and live with them for three years, but start to grow restless and wonder if you can do better. How much do you explore? How much can you explore: now you have a biological time deadline, so you can only try a few dozen options.

There is another term in this literature called “regret”, which again is intuitive, you want to know you made the best possible decision, so that if you look back, you couldn’t have done better.

Although we are concentrating on long-term probabilities, the reward might be changing too. Maybe we have a lot of variance in the payoff : good days and bad days. You can average them. Maybe you really value those great days, science is awesome days. Or maybe you decided you never wanted to have a bad day ever again.

And one more thing to worry about : a lot of real world problems are non-stationarity : the probabilities themselves are changing over time. For example, in the stock market, long-term behavior can be unpredictable, as the world learned last fall. In our date-choosing example, maybe he gets a promotion, starts working out, and shows you he learned that he values you more than you both thought.

Unfortunately, we’re humans, and breakups are usually irreversible, so we can’t go back after decisions sometimes. But this depends on how quickly you, or that person, can forgive. Before you stop talking to someone forever, you might want to just get more exploration. Maybe have lunch together one last time. After all, we have so many things to optimize, regret, exploitation, whatever our loss function is : maybe we are learning the function too. Maybe we discovered that our loss function includes things like financialstatus, intellectual stimulation, cuddliness. Making decisions is hard. But more information usually helps.

You want to minimize your expected loss. For this you need two things : probabilities, and a loss functions. For every possible thing that can happen, calculate how likely it is to happen. This is only half the solution though: then you need to calculate how much that thing means to you if it happens. This is your loss function. Given the two, you can then multiply them, to calculate the expected payoff of every decision-making option. This simple, basic idea is on its way to becoming the dominant theory in cognitive science, economics, and even robotics. For controlling a robot arm, the loss function might be “jerk” – we want to minimize the change in acceleration of the path we take to the target, which will use a minimum amount of energy. Trying to discover the loss function for movement is the mission of my officemate and his lab.

Loss functions are a tricky thing, for example Kahneman won a nobel prize for showing that the loss function for money is not linear: people would much rather take a bet with no risk of losing for less payoff, than a bet with greater payoff but a chance to lose some money. You can work out the probabilities times the amount of money and show mathematically that this is a bad decision, but people make it.

What is your loss function?

And really thinking about all those lonely guys that want to accomplish this: why? I dont think its about cheating death, I think its about finding someone with the brain you like.