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We present a novel quantum algorithm for estimating Gibbs partition functions in sublinear time with respect to the logarithm of the size of the state space. This is the first speed-up of this type to be obtained over the seminal…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…
Partition-wise models offer a flexible approach for modeling complex and multidimensional data that are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
The quality and quantity of data used for training greatly influence the performance and effectiveness of deep learning models. In the context of error correction, it is essential to generate high-quality samples that are neither…
The substantial memory demands of pre-training and fine-tuning large language models (LLMs) require memory-efficient optimization algorithms. One promising approach is layer-wise optimization, which treats each transformer block as a single…
Locality-sensitive hashing (LSH) is a fundamental technique for similarity search and similarity estimation in high-dimensional spaces. The basic idea is that similar objects should produce hash collisions with probability significantly…
Contrastive learning is a representational learning paradigm in which a neural network maps data elements to feature vectors. It improves the feature space by forming lots with an anchor and examples that are either positive or negative…
The Restricted Boltzmann Machines (RBM) can be used either as classifiers or as generative models. The quality of the generative RBM is measured through the average log-likelihood on test data. Due to the high computational complexity of…
The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We…
State-space models have been used in many applications, including econometrics, engineering, medical research, etc. The maximum likelihood estimation (MLE) of the static parameter of general state-space models is not straightforward because…
The density of states for the three-dimensional Ising model is calculated with high-precision from multicanonical simulations. This allows us to estimate the leading partition function zeros for lattice sizes up to L=32. Combining previous…
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…
We consider the problem of unconstrained minimization of a smooth objective function in $\R^n$ in a setting where only function evaluations are possible. While importance sampling is one of the most popular techniques used by machine…
We consider MAP estimators for structured prediction with exponential family models. In particular, we concentrate on the case that efficient algorithms for uniform sampling from the output space exist. We show that under this assumption…
In this paper, we demonstrate the efficiency of simulations via direct computation of the partition function under various macroscopic conditions, such as different temperatures or volumes. The method can compute partition functions by…
A new and efficient algorithm is presented for the calculation of the partition function in the $S=\pm 1$ Ising model. As an example, we use the algorithm to obtain the thermal dependence of the magnetic spin susceptibility of an Ising…