Related papers: Incomplete Reparameterizations and Equivalent Metr…
Mechanistic dynamic models allow for a quantitative and systematic interpretation of data and the generation of testable hypotheses. However, these models are often over-parameterized, leading to non-identifiability and non-observability,…
Minimum-weight perfect matching (MWPM) has been been the primary classical algorithm for error correction in the surface code, since it is of low runtime complexity and achieves relatively low logical error rates [Phys. Rev. Lett. 108,…
In sampling tasks, it is common for target distributions to be known up to a normalizing constant. However, in many situations, even evaluating the unnormalized distribution can be costly or infeasible. This issue arises in scenarios such…
Most of the recent successful applications of neural networks have been based on training with gradient descent updates. However, for some small networks, other mirror descent updates learn provably more efficiently when the target is…
In many hierarchical inverse problems, not only do we want to estimate high- or infinite-dimensional model parameters in the parameter-to-observable maps, but we also have to estimate hyperparameters that represent critical assumptions in…
Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used throughout machine and reinforcement learning; however, they are usually explained as simple mathematical tricks without providing any insight into their nature.…
We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC…
Sufficient statistics are derived for the population size and parameters of commonly used closed population mark-recapture models. Rao-Blackwellization details for improving estimators that are not functions of the statistics are presented.…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
A simple reweighting scheme is proposed for Monte Carlo simulations of interacting particle systems, permitting one to study various parameter values in a single study, and improving efficiency by an order of magnitude. Unlike earlier…
This paper proposes a quantum algorithm for Markov chain spectral gap estimation that is quasi-optimal (i.e., optimal up to a polylogarithmic factor) in the number of vertices for all parameters, and additionally quasi-optimal in the…
Monte Carlo rendering algorithms often utilize correlations between pixels to improve efficiency and enhance image quality. For real-time applications in particular, repeated reservoir resampling offers a powerful framework to reuse samples…
Reparameterization aims to improve the generalization of deep neural networks by transforming convolutional layers into equivalent multi-branched structures during training. However, there exists a gap in understanding how…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
Parameterized complexity allows us to analyze the time complexity of problems with respect to a natural parameter depending on the problem. Reoptimization looks for solutions or approximations for problem instances when given solutions to…
Over-parametrization was a crucial ingredient for recent developments in inference and machine-learning fields. However a good theory explaining this success is still lacking. In this paper we study a very simple case of mismatched…
We study convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (Andrieu and Roberts [Ann. Statist. 37 (2009) 697-725]). We find that the asymptotic variance of the pseudo-marginal algorithm is always at least as…