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Found 13 papers, 0 papers with code
The perils of being unhinged: On the accuracy of classifiers minimizing a noise-robust convex loss
Van Rooyen et al. introduced a notion of convex loss functions being robust to random classification noise, and established that the "unhinged" loss function is robust in this sense.
On the Approximation Power of Two-Layer Networks of Random ReLUs
This paper considers the following question: how well can depth-two ReLU networks with randomly initialized bottom-level weights represent smooth functions?
Quantitative Correlation Inequalities via Semigroup Interpolation
Most correlation inequalities for high-dimensional functions in the literature, such as the Fortuin-Kasteleyn-Ginibre (FKG) inequality and the celebrated Gaussian Correlation Inequality of Royen, are qualitative statements which establish that any two functions of a certain type have non-negative correlation.
Probability Computational Complexity Combinatorics
Efficient average-case population recovery in the presence of insertions and deletions
In this problem, there is an unknown distribution $\cal{D}$ over $s$ unknown source strings $x^1,\dots, x^s \in \{0, 1\}^n$, and each sample is independently generated by drawing some $x^i$ from $\cal{D}$ and returning an independent trace of $x^i$.
Learning from satisfying assignments under continuous distributions
We give a range of efficient algorithms and hardness results for this problem, focusing on the case when $f$ is a low-degree polynomial threshold function (PTF).
Density estimation for shift-invariant multidimensional distributions
This implies that, for constant $d$, multivariate log-concave distributions can be learned in $\tilde{O}_d(1/\epsilon^{2d+2})$ time using $\tilde{O}_d(1/\epsilon^{d+2})$ samples, answering a question of [Diakonikolas, Kane and Stewart, 2016] All of our results extend to a model of noise-tolerant density estimation using Huber's contamination model, in which the target distribution to be learned is a $(1-\epsilon,\epsilon)$ mixture of some unknown distribution in the class with some other arbitrary and unknown distribution, and the learning algorithm must output a hypothesis distribution with total variation distance error $O(\epsilon)$ from the target distribution.
Learning Sums of Independent Random Variables with Sparse Collective Support
For the case $| \mathcal{A} | = 3$, we give an algorithm for learning $\mathcal{A}$-sums to accuracy $\epsilon$ that uses $\mathsf{poly}(1/\epsilon)$ samples and runs in time $\mathsf{poly}(1/\epsilon)$, independent of $N$ and of the elements of $\mathcal{A}$.
Near-Optimal Density Estimation in Near-Linear Time Using Variable-Width Histograms
The "approximation factor" $C$ in our result is inherent in the problem, as we prove that no algorithm with sample size bounded in terms of $k$ and $\epsilon$ can achieve $C<2$ regardless of what kind of hypothesis distribution it uses.
Learning circuits with few negations
In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and the class of all functions.
Efficient Density Estimation via Piecewise Polynomial Approximation
We give an algorithm that draws $\tilde{O}(t\new{(d+1)}/\eps^2)$ samples from $p$, runs in time $\poly(t, d, 1/\eps)$, and with high probability outputs a piecewise polynomial hypothesis distribution $h$ that is $(O(\tau)+\eps)$-close (in total variation distance) to $p$.
Inverse problems in approximate uniform generation
In such an inverse problem, the algorithm is given uniform random satisfying assignments of an unknown function $f$ belonging to a class $\C$ of Boolean functions, and the goal is to output a probability distribution $D$ which is $\epsilon$-close, in total variation distance, to the uniform distribution over $f^{-1}(1)$.
Learning $k$-Modal Distributions via Testing
The learning algorithm is given access to independent samples drawn from an unknown $k$-modal distribution $p$, and it must output a hypothesis distribution $\widehat{p}$ such that with high probability the total variation distance between $p$ and $\widehat{p}$ is at most $\epsilon.$ Our main goal is to obtain \emph{computationally efficient} algorithms for this problem that use (close to) an information-theoretically optimal number of samples.
Learning Poisson Binomial Distributions
Our second main result is a {\em proper} learning algorithm that learns to $\eps$-accuracy using $\tilde{O}(1/\eps^2)$ samples, and runs in time $(1/\eps)^{\poly (\log (1/\eps))} \cdot \log n$.
