For a function K : R^d x R^d -> R, and a set P = {x_1, ...,
x_n} in d-dimension, the K graph G_P of P is the complete graph on
n nodes where the weight between nodes i and j is given by K(x_i,
x_j). In this paper, we initiate the study of when...
I’ll discuss the Noisy Quadratic Model, the toy problem of
minimizing a convex quadratic function with noisy gradient
observations. While the NQM is simple enough to have closed-form
dynamics for a variety of optimizers, it gives a surprising
amount...
Causal inference from observational data is a vital problem, but
it comes with strong assumptions. Most methods require that we
observe all confounders, variables that affect both the causal
variables and the outcome variables. But whether we have...
Function approximators, like deep neural networks, play a
crucial role in building machine-learning based intelligent
systems. This talk covers three core problems of function
approximators: understanding function approximators, designing
new...
This talk presents evidence that humans learn complex functions
by harnessing compositionality: complex structure is decomposed
into simpler building blocks. I formalize this idea in the
framework of Bayesian nonparametric regression using a
grammar...
Online learning is a popular framework for sequential prediction
problems. The standard approach to analyzing an algorithm's
(learner's) performance in online learning is in terms of its
empirical regret defined to be the excess loss suffered by
the...
We make the case that over the coming decade, computer assisted
reasoning will become far more widely used in the mathematical
sciences. This includes interactive and automatic theorem
verification, symbolic algebra, and emerging technologies
such...
The classical regression problem seeks to estimate a function f
on the basis of independent pairs $(x_i,y_i)$ where $\mathbb
E[y_i]=f(x_i)$, $i=1,\dotsc,n$. In this talk, we consider
statistical and computational aspects of the "uncoupled"
version...
Twenty years ago, a link was discovered between the
neurotransmitter dopamine and the computational framework of
reinforcement learning. Since then, it has become well established
that dopamine release reflects a reward prediction error, a
surprise...
