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Found 9 papers, 2 papers with code
Statistical-Computational Trade-offs for Density Estimation
In particular, if an algorithm uses $O(n/\log^c k)$ samples for some constant $c>0$ and polynomial space, then the query time of the data structure must be at least $k^{1-O(1)/\log \log k}$, i. e., close to linear in the number of distributions $k$.
Data Structures for Density Estimation
We study statistical/computational tradeoffs for the following density estimation problem: given $k$ distributions $v_1, \ldots, v_k$ over a discrete domain of size $n$, and sampling access to a distribution $p$, identify $v_i$ that is "close" to $p$.
Learning to Hash Robustly, Guaranteed
In this paper, we design an NNS algorithm for the Hamming space that has worst-case guarantees essentially matching that of theoretical algorithms, while optimizing the hashing to the structure of the dataset (think instance-optimal algorithms) for performance on the minimum-performing query.
Streaming Complexity of SVMs
We show that, for both problems, for dimensions $d=1, 2$, one can obtain streaming algorithms with space polynomially smaller than $\frac{1}{\lambda\epsilon}$, which is the complexity of SGD for strongly convex functions like the bias-regularized SVM, and which is known to be tight in general, even for $d=1$.
Approximate Nearest Neighbor Search in High Dimensions
The nearest neighbor problem is defined as follows: Given a set $P$ of $n$ points in some metric space $(X, D)$, build a data structure that, given any point $q$, returns a point in $P$ that is closest to $q$ (its "nearest neighbor" in $P$).
Subspace Embedding and Linear Regression with Orlicz Norm
An Orlicz norm is parameterized by a non-negative convex function $G:\mathbb{R}_+\rightarrow\mathbb{R}_+$ with $G(0)=0$: the Orlicz norm of a vector $x\in\mathbb{R}^n$ is defined as $ \|x\|_G=\inf\left\{\alpha>0\large\mid\sum_{i=1}^n G(|x_i|/\alpha)\leq 1\right\}.
Approximate Near Neighbors for General Symmetric Norms
We show that every symmetric normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation.
Practical and Optimal LSH for Angular Distance
Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.
A Differential Equations Approach to Optimizing Regret Trade-offs
To obtain our main result, we show that the optimal payoff functions have to satisfy the Hermite differential equation, and hence are given by the solutions to this equation.
