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Found 18 papers, 2 papers with code
Adversarially-Robust Inference on Trees via Belief Propagation
We first confirm a folklore belief that a malicious adversary who can corrupt an inverse-polynomial fraction of the leaves of their choosing makes this inference impossible.
A quasi-polynomial time algorithm for Multi-Dimensional Scaling via LP hierarchies
Multi-dimensional Scaling (MDS) is a family of methods for embedding an $n$-point metric into low-dimensional Euclidean space.
Towards Practical Robustness Auditing for Linear Regression
We investigate practical algorithms to find or disprove the existence of small subsets of a dataset which, when removed, reverse the sign of a coefficient in an ordinary least squares regression involving that dataset.
Fast, Sample-Efficient, Affine-Invariant Private Mean and Covariance Estimation for Subgaussian Distributions
Our algorithm runs in time $\tilde{O}(nd^{\omega - 1} + nd/\varepsilon)$, where $\omega < 2. 38$ is the matrix multiplication exponent.
Robustness Implies Privacy in Statistical Estimation
We study the relationship between adversarial robustness and differential privacy in high-dimensional algorithmic statistics.
Privacy Induces Robustness: Information-Computation Gaps and Sparse Mean Estimation
We establish a simple connection between robust and differentially-private algorithms: private mechanisms which perform well with very high probability are automatically robust in the sense that they retain accuracy even if a constant fraction of the samples they receive are adversarially corrupted.
The Franz-Parisi Criterion and Computational Trade-offs in High Dimensional Statistics
We define a free-energy based criterion for hardness and formally connect it to the well-established notion of low-degree hardness for a broad class of statistical problems, namely all Gaussian additive models and certain models with a sparse planted signal.
A Robust Spectral Algorithm for Overcomplete Tensor Decomposition
We give a spectral algorithm for decomposing overcomplete order-4 tensors, so long as their components satisfy an algebraic non-degeneracy condition that holds for nearly all (all but an algebraic set of measure $0$) tensors over $(\mathbb{R}^d)^{\otimes 4}$ with rank $n \le d^2$.
Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism
SoS proofs to algorithms is a key theme in numerous recent works in high-dimensional algorithmic statistics -- estimators which apparently require exponential running time but whose analysis can be captured by low-degree Sum of Squares proofs can be automatically turned into polynomial-time algorithms with the same provable guarantees.
Statistical Query Algorithms and Low-Degree Tests Are Almost Equivalent
Researchers currently use a number of approaches to predict and substantiate information-computation gaps in high-dimensional statistical estimation problems.
Estimating Rank-One Spikes from Heavy-Tailed Noise via Self-Avoiding Walks
For the case of Gaussian noise, the top eigenvector of the given matrix is a widely-studied estimator known to achieve optimal statistical guarantees, e. g., in the sense of the celebrated BBP phase transition.
Robust and Heavy-Tailed Mean Estimation Made Simple, via Regret Minimization
In this paper, we provide a meta-problem and a duality theorem that lead to a new unified view on robust and heavy-tailed mean estimation in high dimensions.
Robustly Learning any Clusterable Mixture of Gaussians
The key ingredients of this proof are a novel use of SoS-certifiable anti-concentration and a new characterization of pairs of Gaussians with small (dimension-independent) overlap in terms of their parameter distance.
Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detection
In robust mean estimation the goal is to estimate the mean $\mu$ of a distribution on $\mathbb{R}^d$ given $n$ independent samples, an $\varepsilon$-fraction of which have been corrupted by a malicious adversary.
Mean Estimation with Sub-Gaussian Rates in Polynomial Time
We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector.
Statistics Theory Data Structures and Algorithms Statistics Theory
Bayesian estimation from few samples: community detection and related problems
in constant average degree graphs---up to what we conjecture to be the computational threshold for this model.
Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors
For tensor decomposition, we give an algorithm with running time close to linear in the input size (with exponent $\approx 1. 086$) that approximately recovers a component of a random 3-tensor over $\mathbb R^n$ of rank up to $\tilde \Omega(n^{4/3})$.
Tensor principal component analysis via sum-of-squares proofs
We study a statistical model for the tensor principal component analysis problem introduced by Montanari and Richard: Given a order-$3$ tensor $T$ of the form $T = \tau \cdot v_0^{\otimes 3} + A$, where $\tau \geq 0$ is a signal-to-noise ratio, $v_0$ is a unit vector, and $A$ is a random noise tensor, the goal is to recover the planted vector $v_0$.
