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Found 13 papers, 0 papers with code
Semidefinite programs simulate approximate message passing robustly
Approximate message passing (AMP) is a family of iterative algorithms that generalize matrix power iteration.
Spectral clustering in the Gaussian mixture block model
Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex $i$ with a latent feature vector $u_i \in \mathbb{R}^d$ sampled from a mixture of Gaussians, and we add edge $(i, j)$ if and only if the feature vectors are sufficiently similar, in that $\langle u_i, u_j \rangle \ge \tau$ for a pre-specified threshold $\tau$.
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 $n \le d^2$.
Robust Regression Revisited: Acceleration and Improved Estimation Rates
For the general case of smooth GLMs (e. g. logistic regression), we show that the robust gradient descent framework of Prasad et.
Non-asymptotic approximations of neural networks by Gaussian processes
We study the extent to which wide neural networks may be approximated by Gaussian processes when initialized with random weights.
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.
Computational Barriers to Estimation from Low-Degree Polynomials
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data.
High-dimensional estimation via sum-of-squares proofs
On one hand, there is a growing body of work utilizing sum-of-squares proofs for recovering solutions to polynomial systems when the system is feasible.
(Nearly) Efficient Algorithms for the Graph Matching Problem on Correlated Random Graphs
Specifically, for every $\gamma>0$, we give a $n^{O(\log n)}$ time algorithm that given a pair of $\gamma$-correlated $G(n, p)$ graphs $G_0, G_1$ with average degree between $n^{\varepsilon}$ and $n^{1/153}$ for $\varepsilon = o(1)$, recovers the "ground truth" permutation $\pi\in S_n$ that matches the vertices of $G_0$ to the vertices of $G_n$ in the way that minimizes the number of mismatched edges.
Fast and robust tensor decomposition with applications to dictionary learning
We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy.
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 $\tilde \Omega(n^{4/3})$.
Symmetric Tensor Completion from Multilinear Entries and Learning Product Mixtures over the Hypercube
We apply our tensor completion algorithm to the problem of learning mixtures of product distributions over the hypercube, obtaining new algorithmic results.
