Camera-ready version of our NIPS'16 paper.

Learning MNIST digit manifold via variational auto-encoders (implemented in a few lines of keras)

[WIP] Introducing a new generation of online data-driven structured factorizers for massive brain data

DL, the new Bohr model: The thoughts of an irreducible DL troll

In the dawn of the 20th century, most physicists thought Physics had been solved! Thusly, chicken feasts with exquisite wine were organized in labs all around the globe. Then it turned out the Bohr model had serious gaps, and suddenly the party was over, and all lights were put out. DL is the new Bohr model (assuming it is a model at all...), and ICLR2016 looks like a chicken feast :p

Random thoughts on the Lasso (to be continued...)

For any $n$-by-$p$ matrix $X$ (with non-zero rows), consider the following objects
$$\mathcal P_X := \{z \in \mathbb R^n | \|X^Tz\|_\infty \le 1\},\; D_X := \text{diag}(\|X_1\|_\infty,\ldots, \|X_n\|_\infty),\; Z_{D_X} := D_X^{-1}\mathbb B_1,$$
where $\mathbb B_1$ is the unit-ball for the $\ell_1$-norm.  Note that $Z_{D_X} \subseteq \mathcal P_X$.

Given a closed convex set $K \subseteq \mathbb R^n$, we've defined the euclidean projection
$$\text{proj}_K(a) := \text{the unique point of }K\text{ minimizing distance from }a \text{ to } K.$$
It's not (too) hard prove that $0 \le QP \le QA$.

What more (of geometric taste) can be said about the picture ?

$\frac{1}{2}\|.\|^2$ is the only self-dual function on a Hilbert space $X$!

Let $X$ be a Hibert space, $x \mapsto \|x\| := \sqrt{x^Tx}$ be the euclidean norm on $X$, and $f:X \rightarrow (-\infty,+\infty]$ an extended real-valued function. Define the convex conjugate of $f$, denoted $f^*$, by
$$f^*(y) := \sup_{x \in X}x^Ty - f(x), \; \forall y \in X.$$
Note that $f^*$ is always convex l.s.c (being the supremum of affine functions) without any assumptions whatsoever on $f$.

Question: When do we have $f^* = f$ ? Checkout the answer here.

Paper accepted at ICASSP 2016!

Our math paper entitled: "LOCAL Q-LINEAR CONVERGENCE AND FINITE-TIME ACTIVE SET IDENTIFICATION OF ADMM ON A CLASS OF PENALIZED REGRESSION PROBLEMS" has been accepted for the ICASSP 2016 signal-processing conference (the largest in the world). The conference will be held at the shicc (Shanghai Convention Center).

Author manuscript available upon demand.