Indeed, this is a central question of recent workstudyinggeneralized lowrankmodels.

In addition, we present an alternative design that permits a near-optimal sublinear decoding timeofO(klog2k+klogn).

Leveraging this result, our work provides the first provably efficient implementation of PseudoPML.

Ineachstep, A's output distribution is within ζ of the true distribution N(t,1;S). Consider a hypothetical sampling algorithm A0 in which A is run, and then the output is altered by rejection to match the true distribution.

Ourresult follows from a statistical and computational analysis of the Stochastic Gradient Descent (SGD) algorithm for solving a natural adaptation of the LASSO optimization problem that accommodates truncation.

Regarding computational aspects of PML, [CSS19a] provided the first efficient algorithm with a non-trivialapproximation guarantee ofexp( n2/3logn),which further implied asample optimal universal estimator forn 1/6.

Regarding computational aspects of PML, [CSS19a] provided the first efficient algorithm with a non-trivialapproximation guarantee ofexp( n2/3logn),which further implied asample optimal universal estimator forn 1/6.

Aconcrete example ofthisisthe"Gaussian Gated Linear Networks" paper (which can7 be found on arXiv) that shows SOTA results on many regression problems. We agree that the continual learning problem is far more complex than captured by current14 standard datasets. ImageNet), but it's worth noting that (1) the two fields are solving very different problems, and (2) that even17 MNIST variants are sufficiently complextoclearly stratify the performance ofcompeting methods (the function of18 a challenge dataset). There is a slight misunderstanding regarding the asymptotic time complexity of the algorithm.42

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples $(\mathbf{x},y)$ from an unknown distribution on $\mathbb{R}^n \times \{ \pm 1\}$, whose marginal distribution on $\mathbf{x}$ is the standard Gaussian and the labels $y$ can be arbitrary, the goal is to output a hypothesis with 0-1 loss $\mathrm{OPT}+\epsilon$, where $\mathrm{OPT}$ is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.