P. Dayan. Recognition in hierarchical models. In F. Cucker and M. Shub, editors, Foundations of Computational Mathematics. Springer, Berlin, Germany, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....has a direct connection to Monte Carlo methods widely used in engineering. These methods use built in randomness to solve difficult problems that cannot be solved analytically. In particular, such methods are one of the main options for performing approximate inference in Bayesian networks [11]. With that in mind, it is perhaps even a bit surprising that Monte Carlo sampling has not, to our knowledge, previously been suggested as an explanation for the randomness of neural responses. Although the approach proposed is not specific to sensory modality, we will here, for concreteness, ....

.... only a single point (at the maximum) Such a representation cannot adequately represent multimodal posterior distributions, nor does it provide any way of coding the uncertainty of the value (the width of the peak) Many other proposed neural representations of probabilities face similar problems [11] (however, see [15] for a recent interesting approach to representing distributions) Indeed, it has been said [10, 16] that how probabilities actually are represented in the brain is one of the most important unanswered questions in the probabilistic approach to perception. In the next section we ....

[Article contains additional citation context not shown here]

P. Dayan. Recognition in hierarchical models. In F. Cucker and M. Shub, editors, Foundations of Computational Mathematics. Springer, Berlin, Germany, 1997.

....equally well view these tests are just part of our observations, and the diseases as our explanations for the combination of observed symptoms and test results. 32 models it is impossible (even in theory) to know the precise values of s, so one must be content with a probability density p(s x) [29]. By Bayes rule, this is given as p(s x) p(x s)p(s) p(x) 6.2) To obtain a point estimate of the hidden variables, many models simply opt to find the particular s which maximize this density, s = arg max p(s x) 6.3) The connection to analysis by synthesis should now be clear: the ....

P. Dayan, "Recognition in hierarchical models," in Foundations of Computational Mathematics (F. Cucker and M. Shub, eds.), Springer, 1997.

....equally well view these tests are just part of our observations, and the diseases as our explanations for the combination of observed symptoms and test results. 32 models it is impossible (even in theory) to know the precise values of s, so one must be content with a probability density p(s x) [29]. By Bayes rule, this is given as p(s x) p(x s)p(s) p(x) 6.2) To obtain a point estimate of the hidden variables, many models simply opt to find the particular s which maximize this density, s = arg max p(s x) 6.3) The connection to analysis by synthesis should now be clear: the ....

P. Dayan, "Recognition in hierarchical models," in Foundations of Computational Mathematics (F. Cucker and M. Shub, eds.), Springer, 1997.

....has a direct connection to Monte Carlo methods widely used in engineering. These methods use built in randomness to solve difficult problems that cannot be solved analytically. In particular, such methods are one of the main options for performing approximate inference in Bayesian networks [11]. With that in mind, it is perhaps even a bit surprising that Monte Carlo sampling has not, to our knowledge, previously been suggested as an explanation for the randomness of neural responses. Although the approach proposed is not specific to sensory modality, we will here, for concreteness, ....

.... only a single point (at the maximum) Such a representation cannot adequately represent multimodal posterior distributions, nor does it provide any way of coding the uncertainty of the value (the width of the peak) Many other proposed neural representations of probabilities face similar problems [11] (however, see [15] for a recent interesting approach to representing distributions) Indeed, it has been said [10, 16] that how probabilities actually are represented in the brain is one of the most important unanswered questions in the probabilistic approach to perception. In the next section we ....

[Article contains additional citation context not shown here]

P. Dayan. Recognition in hierarchical models. In F. Cucker and M. Shub, editors, Foundations of Computational Mathematics. Springer, Berlin, Germany, 1997.

No context found.

Dayan, P (1997). Recognition in hierarchical models. In F Cucker & M Shub, editors, Foundations of Computational Mathematics. Berlin, Germany: Springer.

No context found.

Dayan, P (1997). Recognition in hierarchical models. In F Cucker & M Shub, editors, Foundations of Computational Mathematics. Berlin, Germany: Springer.

No context found.

P. Dayan. Recognition in hierarchical models. In F. Cucker and M. Shub, editors, Foundations of Computational Mathematics. Springer, Berlin, Germany, 1997.

No context found.

P. Dayan. Recognition in hierarchical models. In F. Cucker and M. Shub, editors, Foundations of Computational Mathematics. Springer, Berlin, Germany, 1997.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC