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Found 26 papers, 4 papers with code
Convergence Bounds for Sequential Monte Carlo on Multimodal Distributions using Soft Decomposition
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.
Learning Mixtures of Gaussians Using Diffusion Models
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.
How Flawed Is ECE? An Analysis via Logit Smoothing
Informally, a model is calibrated if its predictions are correct with a probability that matches the confidence of the prediction.
Principled Gradient-based Markov Chain Monte Carlo for Text Generation
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.
Improved Bound for Mixing Time of Parallel Tempering
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.
Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions
We give an improved theoretical analysis of score-based generative modeling.
Fisher information lower bounds for sampling
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.
Pitfalls of Gaussians as a noise distribution in NCE
Noise Contrastive Estimation (NCE) is a popular approach for learning probability density functions parameterized up to a constant of proportionality.
Convergence of score-based generative modeling for general data distributions
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.
Convergence for score-based generative modeling with polynomial complexity
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.
Sampling Approximately Low-Rank Ising Models: MCMC meets Variational Methods
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.
Universal Approximation Using Well-Conditioned Normalizing Flows
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
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
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
Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory.
Efficient sampling from the Bingham distribution
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
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
Estimating the normalizing constant of an unnormalized probability distribution has important applications in computer science, statistical physics, machine learning, and statistics.
Explaining Landscape Connectivity of Low-cost Solutions for Multilayer Nets
Mode connectivity is a surprising phenomenon in the loss landscape of deep nets.
Robust guarantees for learning an autoregressive filter
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.
Online Sampling from Log-Concave Distributions
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
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
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
We study the control of symmetric linear dynamical systems with unknown dynamics and a hidden state.
Beyond Log-concavity: Provable Guarantees for Sampling Multi-modal Distributions using Simulated Tempering Langevin Monte Carlo
We analyze this Markov chain for the canonical multi-modal distribution: a mixture of gaussians (of equal variance).
On the ability of neural nets to express distributions
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.
