Related papers: Towards algebraic methods for maximum entropy esti…
In this paper, it is shown that an auto-encoder using optimal reconstruction significantly outperforms a conventional auto-encoder. Optimal reconstruction uses the conditional mean of the input given the features, under a maximum entropy…
The maximum likelihood method is the best-known method for estimating the probabilities behind the data. However, the conventional method obtains the probability model closest to the empirical distribution, resulting in overfitting. Then…
We discuss the problems of applying Maximum Likelihood methods to the CMB and how one can make it both efficient and optimal. The solution is a generalised eigenvalue problem that allows virtually no loss of information about the parameter…
We use maximal entropy methods to examine the distribution properties of primitive integer points on spheres and of CM points on the modular surface. The proofs we give are a modern and dynamical interpretation of Linnik's original ideas…
We study existence and computability of finite bases for ideals of polynomials over infinitely many variables. In our setting, variables come from a countable logical structure A, and embeddings from A to A act on polynomials by renaming…
New experimental methods make it possible to measure the expression levels of many genes, simultaneously, in snapshots from thousands or even millions of individual cells. Current approaches to analyze these experiments involve clustering…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
There are three ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a…
Gathering the most information by picking the least amount of data is a common task in experimental design or when exploring an unknown environment in reinforcement learning and robotics. A widely used measure for quantifying the…
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…
Flexibility in shape and scale of Burr XII distribution can make close approximation of numerous well-known probability density functions. Due to these capabilities, the usages of Burr XII distribution are applied in risk analysis, lifetime…
For a multinomial distribution, suppose that we have prior knowledge of the sum of the probabilities of some categories. This allows us to construct a submodel in a full (i.e., no-restriction) model. Maximum likelihood estimation (MLE)…
In this paper, we study the maximum entropy sampling problem (MESP) and its variants. MESP seeks to identify a small subset of variables that maximizes the determinant of a covariance submatrix, and is a fundamental model in optimal…
We introduce an algebraic multiscale method for two--dimensional problems. The method uses the generalized multiscale finite element method based on the quadrilateral nonconforming finite element spaces. Differently from the…
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded Quantum Inverse Scattering Method. The Bethe ansatz equations for all these models are derived by using the algebraic…
We present an algebraic approach to evolutionary accumulation modelling (EvAM). EvAM is concerned with learning and predicting the order in which evolutionary features accumulate over time. Our approach is complementary to the more common…
A first-principle multiscale modeling approach is presented, which is derived from the solution of the Ornstein-Zernike equation for the coarse-grained representation of polymer liquids. The approach is analytical, and for this reason is…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
Stochastic differential equations such as the Ornstein-Uhlenbeck process have long been used to model realworld probablistic events such as stock prices and temperature fluctuations. While statistical methods such as Maximum Likelihood…
We tackle covariance estimation in low-sample scenarios, employing a structured covariance matrix with shrinkage methods. These involve convexly combining a low-bias/high-variance empirical estimate with a biased regularization estimator,…