no code implementations • 29 May 2024 • Holden Lee, Matheau Santana-Gijzen

We prove bounds on the variance of a function $f$ under the empirical measure of the samples obtained by the Sequential Monte Carlo (SMC) algorithm, with time complexity depending on local rather than global Markov chain mixing dynamics.

no code implementations • 29 Apr 2024 • Khashayar Gatmiry, Jonathan Kelner, Holden Lee

We give a new algorithm for learning mixtures of $k$ Gaussians (with identity covariance in $\mathbb{R}^n$) to TV error $\varepsilon$, with quasi-polynomial ($O(n^{\text{poly log}\left(\frac{n+k}{\varepsilon}\right)})$) time and sample complexity, under a minimum weight assumption.

1 code implementation • 15 Feb 2024 • Muthu Chidambaram, Holden Lee, Colin McSwiggen, Semon Rezchikov

Informally, a model is calibrated if its predictions are correct with a probability that matches the confidence of the prediction.

no code implementations • 29 Dec 2023 • Li Du, Afra Amini, Lucas Torroba Hennigen, Xinyan Velocity Yu, Jason Eisner, Holden Lee, Ryan Cotterell

Recent papers have demonstrated the possibility of energy-based text generation by adapting gradient-based sampling algorithms, a paradigm of MCMC algorithms that promises fast convergence.

no code implementations • 3 Apr 2023 • Holden Lee, Zeyu Shen

In this paper, we present a new lower bound for parallel tempering on the spectral gap that has a polynomial dependence on all parameters except $\log L$, where $(L + 1)$ is the number of levels.

no code implementations • 3 Nov 2022 • Hongrui Chen, Holden Lee, Jianfeng Lu

We give an improved theoretical analysis of score-based generative modeling.

no code implementations • 5 Oct 2022 • Sinho Chewi, Patrik Gerber, Holden Lee, Chen Lu

We prove two lower bounds for the complexity of non-log-concave sampling within the framework of Balasubramanian et al. (2022), who introduced the use of Fisher information (FI) bounds as a notion of approximate first-order stationarity in sampling.

no code implementations • 1 Oct 2022 • Holden Lee, Chirag Pabbaraju, Anish Sevekari, Andrej Risteski

Noise Contrastive Estimation (NCE) is a popular approach for learning probability density functions parameterized up to a constant of proportionality.

no code implementations • 26 Sep 2022 • Holden Lee, Jianfeng Lu, Yixin Tan

Score-based generative modeling (SGM) has grown to be a hugely successful method for learning to generate samples from complex data distributions such as that of images and audio.

no code implementations • 13 Jun 2022 • Holden Lee, Jianfeng Lu, Yixin Tan

Using our guarantee, we give a theoretical analysis of score-based generative modeling, which transforms white-noise input into samples from a learned data distribution given score estimates at different noise scales.

no code implementations • 17 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.

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?

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?

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.

1 code implementation • 19 Nov 2020 • Holden Lee

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

no code implementations • 30 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 code implementations • 6 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.

no code implementations • 8 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.

1 code implementation • NeurIPS 2019 • Rohith Kuditipudi, Xiang Wang, Holden Lee, Yi Zhang, Zhiyuan Li, Wei Hu, Sanjeev Arora, Rong Ge

Mode connectivity is a surprising phenomenon in the loss landscape of deep nets.

no code implementations • 23 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.

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.

no code implementations • 29 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").

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.

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.

no code implementations • NeurIPS 2018 • Rong Ge, Holden Lee, Andrej Risteski

We analyze this Markov chain for the canonical multi-modal distribution: a mixture of gaussians (of equal variance).

no code implementations • 22 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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