209 karma · joined November 26, 2013
In Kalman filters, you assume the unobserved state is Gaussian-ish and it moves continuously according to linear-ish dynamics (depending on which flavor of Kalman filter is being used).
In HMMs, you assume the hidden state is one of a few classes, and the movement among these states uses a discrete Markov chain.
In my experience, the algorithms are often pretty different for these two cases, but the underlying idea is very similar.
[0]: http://www.wsj.com/articles/SB100014240531119034809045765122...
"I believe there are 15 747 724 136 275 002 577 605 653 961 181 555 468 044 717 914 527 116 709 366 231 425 076 185 631 031 296 protons in the universe and the same number of electrons." --Sir Arthur Eddington
That's not the part that's "stochastic"; sensitivity to initial conditions is just nonconvex optimization in action. You get the same thing with most other local embeddings.
The stochastic bit is that the model is based on optimizing "the asymmetric probability, pij , that i would pick j as its neighbor"[0]. Those probabilities and the associated positions in 2D space are not estimated stochastically (e.g. with Monte Carlo sampling) or anything, though.
This is mostly true, but last time I checked, Stan still couldn't sample discrete variables like BUGS can. Stan can only fit models with discrete parameters (e.g. finite mixtures) if the programmer is smart enough to integrate them out.
I was referring more specifically to the fact that Nature had to enlist volunteers to referee the paper he wrote.
I was curious whether he was okay with that even though he wouldn't volunteer himself, if his position on non-open journals had changed, or if there was some other explanation.
I had assumed that meant he wouldn't write for them either (and thus wouldn't enlist other people to volunteer as reviewers when the final product would cost $32 to read).
Apart from the chemistry part (where I don't understand what you mean), biology has had this for 85 years, with numerous extensions and generalizations [1].
Almost all of that time was spent in Africa. Even during glacial periods, was it ever icy? I don't know much about the paleoclimate, so I'm not sure.
I'd love to see reports of basic genetic genetic properties of the population. What's the variance in fitness within each generation? This turns out to be the key factor in the rate of evolution [1], assuming that one defines fitness the way that geneticists do.
Also, estimates of the relative strengths of mutation, selection, and drift would be nice, as would options for distinguishing between hard and soft selection. These sorts of diagnostics and options could really improve the method's effectiveness.
[1] https://en.wikipedia.org/wiki/Fisher%27s_fundamental_theorem...
I haven't looked into the math myself, but apparently there are situations where the increase in representational power for networks of a given size can be increased exponentially by moving nodes into higher layers.
The write-up is a bit misleading, though: the model in their preprint[1] is about stacks of restricted Boltzmann machines (RBMs), and are very different from the other examples of deep learning mentioned. The Google Cat Detector model, for example, didn't describe a probability distribution over images, which is the kind of task that the preprint is about. And in almost all of the recent cases where deep neural networks have made substantial progress over the previous state of the art, the models have not been probabilistic, or trained layer-by-layer, or unsupervised, like the RBM-based approach in the preprint.
I don't speak physics, but my reading of the paper says that could be summarized pretty accurately as follows:
1. Hinton et al. (2006) showed that each layer in a stack of RBMs improves a variational lower bound on p(x).
2. Variational methods for RG also iteratively improve a variational lower bound on p(x).
3. The two methods would thus be equivalent, if we could fit them without error (which we can't).
4. Here’s a figure from a stack of RBMs that vaguely looks like RG results (not shown)
I don't see any comparison between the approximations that physicists normally use versus the contrastive divergence for training RBM-based networks, or evidence that their results are more similar in practice than any other technique.
Am I missing something?
[1] http://arxiv.org/abs/1410.3831 [2] https://www.cs.toronto.edu/~hinton/absps/fastnc.pdf
>Detroit just watched its last mainstream grocer, Farmer Jack, close its doors for good.
[1] http://www.npr.org/templates/story/story.php?storyId=1247787...