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Found 20 papers, 1 papers with code
Private Vector Mean Estimation in the Shuffle Model: Optimal Rates Require Many Messages
We study the problem of private vector mean estimation in the shuffle model of privacy where $n$ users each have a unit vector $v^{(i)} \in\mathbb{R}^d$.
Lower Bounds for Differential Privacy Under Continual Observation and Online Threshold Queries
One of the most basic problems for studying the "price of privacy over time" is the so called private counter problem, introduced by Dwork et al. (2010) and Chan et al. (2010).
Hot PATE: Private Aggregation of Distributions for Diverse Task
Until now, PATE has primarily been explored with classification-like tasks, where each example possesses a ground-truth label, and knowledge is transferred to the student by labeling public examples.
Sparse Dimensionality Reduction Revisited
In this work, we revisit sparse embeddings and identify a loophole in the lower bound.
Õptimal Differentially Private Learning of Thresholds and Quasi-Concave Optimization
The problem of learning threshold functions is a fundamental one in machine learning.
Tricking the Hashing Trick: A Tight Lower Bound on the Robustness of CountSketch to Adaptive Inputs
When inputs are adaptive, however, an adversarial input can be constructed after $O(\ell)$ queries with the classic estimator and the best known robust estimator only supports $\tilde{O}(\ell^2)$ queries.
Estimation of Entropy in Constant Space with Improved Sample Complexity
Recent work of Acharya et al. (NeurIPS 2019) showed how to estimate the entropy of a distribution $\mathcal D$ over an alphabet of size $k$ up to $\pm\epsilon$ additive error by streaming over $(k/\epsilon^3) \cdot \text{polylog}(1/\epsilon)$ i. i. d.
Uniform Approximations for Randomized Hadamard Transforms with Applications
We use our inequality to then derive improved guarantees for two applications in the high-dimensional regime: 1) kernel approximation and 2) distance estimation.
Private Frequency Estimation via Projective Geometry
In many parameter settings used in practice this is a significant improvement over the $ O(n+k^2)$ computation cost that is achieved by the recent PI-RAPPOR algorithm (Feldman and Talwar; 2021).
On the Robustness of CountSketch to Adaptive Inputs
CountSketch is a popular dimensionality reduction technique that maps vectors to a lower dimension using randomized linear measurements.
Terminal Embeddings in Sublinear Time
\end{equation*} When $X, Y$ are both Euclidean metrics with $Y$ being $m$-dimensional, recently (Narayanan, Nelson 2019), following work of (Mahabadi, Makarychev, Makarychev, Razenshteyn 2018), showed that distortion $1+\epsilon$ is achievable via such a terminal embedding with $m = O(\epsilon^{-2}\log n)$ for $n := |T|$.
Randomized Algorithms for Scientific Computing (RASC)
Randomized algorithms have propelled advances in artificial intelligence and represent a foundational research area in advancing AI for Science.
On Adaptive Distance Estimation
Our memory consumption is $\tilde O((n+d)d/\epsilon^2)$, slightly more than the $O(nd)$ required to store $X$ in memory explicitly, but with the benefit that our time to answer queries is only $\tilde O(\epsilon^{-2}(n + d))$, much faster than the naive $\Theta(nd)$ time obtained from a linear scan in the case of $n$ and $d$ very large.
Data Structures and Algorithms
Margin-Based Generalization Lower Bounds for Boosted Classifiers
To date, the strongest known generalization (upper bound) is the $k$th margin bound of Gao and Zhou (2013).
Optimal terminal dimensionality reduction in Euclidean space
$$ We show that a strictly stronger version of this statement holds, answering one of the main open questions of [MMMR18]: "$\forall y\in X$" in the above statement may be replaced with "$\forall y\in\mathbb R^d$", so that $f$ not only preserves distances within $X$, but also distances to $X$ from the rest of space.
Heavy hitters via cluster-preserving clustering
Our main innovation is an efficient reduction from the heavy hitters to a clustering problem in which each heavy hitter is encoded as some form of noisy spectral cluster in a much bigger graph, and the goal is to identify every cluster.
An improved analysis of the ER-SpUD dictionary learning algorithm
Then, given some small number $p$ of samples, i. e.\ columns of $Y$, the goal is to learn the dictionary $A$ up to small error, as well as $X$.
Optimal approximate matrix product in terms of stable rank
We prove, using the subspace embedding guarantee in a black box way, that one can achieve the spectral norm guarantee for approximate matrix multiplication with a dimensionality-reducing map having $m = O(\tilde{r}/\varepsilon^2)$ rows.
Toward a unified theory of sparse dimensionality reduction in Euclidean space
Let $\Phi\in\mathbb{R}^{m\times n}$ be a sparse Johnson-Lindenstrauss transform [KN14] with $s$ non-zeroes per column.
Fast Moment Estimation in Data Streams in Optimal Space
We give a space-optimal algorithm with update time O(log^2(1/eps)loglog(1/eps)) for (1+eps)-approximating the pth frequency moment, 0 < p < 2, of a length-n vector updated in a data stream.
Data Structures and Algorithms
