Search Results for author: Holden Lee

Found 16 papers, 3 papers with code

Sampling Approximately Low-Rank Ising Models: MCMC meets Variational Methods

no code implementations17 Feb 2022 Frederic Koehler, Holden Lee, Andrej Risteski

We consider Ising models on the hypercube with a general interaction matrix $J$, and give a polynomial time sampling algorithm when all but $O(1)$ eigenvalues of $J$ lie in an interval of length one, a situation which occurs in many models of interest.

Variational Inference

Universal Approximation Using Well-Conditioned Normalizing Flows

no code implementations NeurIPS 2021 Holden Lee, Chirag Pabbaraju, Anish Prasad Sevekari, Andrej Risteski

As ill-conditioned Jacobians are an obstacle for likelihood-based training, the fundamental question remains: which distributions can be approximated using well-conditioned affine coupling flows?

Universal Approximation for Log-concave Distributions using Well-conditioned Normalizing Flows

no code implementations ICML Workshop INNF 2021 Holden Lee, Chirag Pabbaraju, Anish Sevekari, Andrej Risteski

As ill-conditioned Jacobians are an obstacle for likelihood-based training, the fundamental question remains: which distributions can be approximated using well-conditioned affine coupling flows?

Improved rates for prediction and identification for partially observed linear dynamical systems

no code implementations NeurIPS 2021 Holden Lee

Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory.

Improved rates for prediction and identification of partially observed linear dynamical systems

1 code implementation19 Nov 2020 Holden Lee

Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory.

Efficient sampling from the Bingham distribution

no code implementations30 Sep 2020 Rong Ge, Holden Lee, Jianfeng Lu, Andrej Risteski

We give a algorithm for exact sampling from the Bingham distribution $p(x)\propto \exp(x^\top A x)$ on the sphere $\mathcal S^{d-1}$ with expected runtime of $\operatorname{poly}(d, \lambda_{\max}(A)-\lambda_{\min}(A))$.

No-Regret Prediction in Marginally Stable Systems

no code implementations6 Feb 2020 Udaya Ghai, Holden Lee, Karan Singh, Cyril Zhang, Yi Zhang

This requires a refined regret analysis, including a structural lemma showing the current state of the system to be a small linear combination of past states, even if the state grows polynomially.

Estimating Normalizing Constants for Log-Concave Distributions: Algorithms and Lower Bounds

no code implementations8 Nov 2019 Rong Ge, Holden Lee, Jianfeng Lu

Estimating the normalizing constant of an unnormalized probability distribution has important applications in computer science, statistical physics, machine learning, and statistics.

Robust guarantees for learning an autoregressive filter

no code implementations23 May 2019 Holden Lee, Cyril Zhang

The optimal predictor for a linear dynamical system (with hidden state and Gaussian noise) takes the form of an autoregressive linear filter, namely the Kalman filter.

Time Series Time Series Prediction

Online Sampling from Log-Concave Distributions

1 code implementation NeurIPS 2019 Holden Lee, Oren Mangoubi, Nisheeth K. Vishnoi

Given a sequence of convex functions $f_0, f_1, \ldots, f_T$, we study the problem of sampling from the Gibbs distribution $\pi_t \propto e^{-\sum_{k=0}^tf_k}$ for each epoch $t$ in an online manner.

Simulated Tempering Langevin Monte Carlo II: An Improved Proof using Soft Markov Chain Decomposition

no code implementations29 Nov 2018 Rong Ge, Holden Lee, Andrej Risteski

Previous approaches rely on decomposing the state space as a partition of sets, while our approach can be thought of as decomposing the stationary measure as a mixture of distributions (a "soft partition").

Spectral Filtering for General Linear Dynamical Systems

no code implementations NeurIPS 2018 Elad Hazan, Holden Lee, Karan Singh, Cyril Zhang, Yi Zhang

We give a polynomial-time algorithm for learning latent-state linear dynamical systems without system identification, and without assumptions on the spectral radius of the system's transition matrix.

Towards Provable Control for Unknown Linear Dynamical Systems

no code implementations ICLR 2018 Sanjeev Arora, Elad Hazan, Holden Lee, Karan Singh, Cyril Zhang, Yi Zhang

We study the control of symmetric linear dynamical systems with unknown dynamics and a hidden state.

On the ability of neural nets to express distributions

no code implementations22 Feb 2017 Holden Lee, Rong Ge, Tengyu Ma, Andrej Risteski, Sanjeev Arora

We take a first cut at explaining the expressivity of multilayer nets by giving a sufficient criterion for a function to be approximable by a neural network with $n$ hidden layers.

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