Search Results for author:
Found 23 papers, 0 papers with code
Optimal high-precision shadow estimation
We give the first tight sample complexity bounds for shadow tomography and classical shadows in the regime where the target error is below some sufficiently small inverse polynomial in the dimension of the Hilbert space.
Structure learning of Hamiltonians from real-time evolution
We study the problem of Hamiltonian structure learning from real-time evolution: given the ability to apply $e^{-\mathrm{i} Ht}$ for an unknown local Hamiltonian $H = \sum_{a = 1}^m \lambda_a E_a$ on $n$ qubits, the goal is to recover $H$.
An optimal tradeoff between entanglement and copy complexity for state tomography
In this work, we study tomography in the natural setting where one can make measurements of $t$ copies at a time.
Learning quantum Hamiltonians at any temperature in polynomial time
Anshu, Arunachalam, Kuwahara, and Soleimanifar (arXiv:2004. 07266) gave an algorithm to learn a Hamiltonian on $n$ qubits to precision $\epsilon$ with only polynomially many copies of the Gibbs state, but which takes exponential time.
Matrix Completion in Almost-Verification Time
In the well-studied setting where $\mathbf{M}$ has incoherent row and column spans, our algorithms complete $\mathbf{M}$ to high precision from $mr^{2+o(1)}$ observations in $mr^{3 + o(1)}$ time (omitting logarithmic factors in problem parameters), improving upon the prior state-of-the-art [JN15] which used $\approx mr^5$ samples and $\approx mr^7$ time.
Tensor Decompositions Meet Control Theory: Learning General Mixtures of Linear Dynamical Systems
In this work we give a new approach to learning mixtures of linear dynamical systems that is based on tensor decompositions.
A New Approach to Learning Linear Dynamical Systems
Linear dynamical systems are the foundational statistical model upon which control theory is built.
Minimax Rates for Robust Community Detection
In this work, we study the problem of community detection in the stochastic block model with adversarial node corruptions.
When Does Adaptivity Help for Quantum State Learning?
We give an adaptive algorithm that outputs a state which is $\gamma$-close in infidelity to $\rho$ using only $\tilde{O}(d^3/\gamma)$ copies, which is optimal for incoherent measurements.
Tight Bounds for Quantum State Certification with Incoherent Measurements
When $\sigma$ is the maximally mixed state $\frac{1}{d} I_d$, this is known as mixedness testing.
Semi-Random Sparse Recovery in Nearly-Linear Time
We design a new iterative method tailored to the geometry of sparse recovery which is provably robust to our semi-random model.
The Pareto Frontier of Instance-Dependent Guarantees in Multi-Player Multi-Armed Bandits with no Communication
We ask whether it is possible to obtain optimal instance-dependent regret $\tilde{O}(1/\Delta)$ where $\Delta$ is the gap between the $m$-th and $m+1$-st best arms.
Robust Voting Rules from Algorithmic Robust Statistics
Maximum likelihood estimation furnishes powerful insights into voting theory, and the design of voting rules.
Clustering Mixtures with Almost Optimal Separation in Polynomial Time
We give the first algorithm which runs in polynomial time, and which almost matches this guarantee.
Margin-Independent Online Multiclass Learning via Convex Geometry
We consider the problem of multi-class classification, where a stream of adversarially chosen queries arrive and must be assigned a label online.
Robust Model Selection and Nearly-Proper Learning for GMMs
Given $\textsf{poly}(k/\epsilon)$ samples from a distribution that is $\epsilon$-close in TV distance to a GMM with $k$ components, we can construct a GMM with $\widetilde{O}(k)$ components that approximates the distribution to within $\widetilde{O}(\epsilon)$ in $\textsf{poly}(k/\epsilon)$ time.
Algorithms from Invariants: Smoothed Analysis of Orbit Recovery over $SO(3)$
Our main result is a quasi-polynomial time algorithm for orbit recovery over $SO(3)$ in this model.
Learning GMMs with Nearly Optimal Robustness Guarantees
In this work we solve the problem of robustly learning a high-dimensional Gaussian mixture model with $k$ components from $\epsilon$-corrupted samples up to accuracy $\widetilde{O}(\epsilon)$ in total variation distance for any constant $k$ and with mild assumptions on the mixture.
Myersonian Regression
Motivated by pricing applications in online advertising, we study a variant of linear regression with a discontinuous loss function that we term Myersonian regression.
Settling the Robust Learnability of Mixtures of Gaussians
This work represents a natural coalescence of two important lines of work: learning mixtures of Gaussians and algorithmic robust statistics.
Tensor Completion Made Practical
We show strong provable guarantees, including showing that our algorithm converges linearly to the true tensors even when the factors are highly correlated and can be implemented in nearly linear time.
Optimal Contextual Pricing and Extensions
We provide a generic algorithm with $O(d^2)$ regret where $d$ is the covering dimension of this class.
Efficiently Learning Mixtures of Mallows Models
Mixtures of Mallows models are a popular generative model for ranking data coming from a heterogeneous population.
