Related papers: Convergence of Discrete MDL for Sequential Predict…
Complexity is a fundamental concept underlying statistical learning theory that aims to inform generalization performance. Parameter count, while successful in low-dimensional settings, is not well-justified for overparameterized settings…
Over the years, ensemble methods have become a staple of machine learning. Similarly, generalized linear models (GLMs) have become very popular for a wide variety of statistical inference tasks. The former have been shown to enhance out-…
The normalized maximized likelihood (NML) provides the minimax regret solution in universal data compression, gambling, and prediction, and it plays an essential role in the minimum description length (MDL) method of statistical modeling…
Robust low-rank matrix estimation is a topic of increasing interest, with promising applications in a variety of fields, from computer vision to data mining and recommender systems. Recent theoretical results establish the ability of such…
Many regression problems involve not one but several response variables (y's). Often the responses are suspected to share a common underlying structure, in which case it may be advantageous to share information across them; this is known as…
In the Minimum Description Length (MDL) principle, learning from the data is equivalent to an optimal coding problem. We show that the codes that achieve optimal compression in MDL are critical in a very precise sense. First, when they are…
Solomonoff's general theory of inference and the Minimum Description Length principle formalize Occam's razor, and hold that a good model of data is a model that is good at losslessly compressing the data, including the cost of describing…
We investigate the detectability of modules in large networks when the number of modules is not known in advance. We employ the minimum description length (MDL) principle which seeks to minimize the total amount of information required to…
Solomonoff's uncomputable universal prediction scheme $\xi$ allows to predict the next symbol $x_k$ of a sequence $x_1...x_{k-1}$ for any Turing computable, but otherwise unknown, probabilistic environment $\mu$. This scheme will be…
This paper extends the work in [Suzuki, 1996] and presents an efficient depth-first branch-and-bound algorithm for learning Bayesian network structures, based on the minimum description length (MDL) principle, for a given (consistent)…
We tackle the problem of penalty selection of regularization on the basis of the minimum description length (MDL) principle. In particular, we consider that the design space of the penalty function is high-dimensional. In this situation,…
We consider the fundamental problem of inferring the causal direction between two univariate numeric random variables $X$ and $Y$ from observational data. The two-variable case is especially difficult to solve since it is not possible to…
Deep metric learning (DML) aims to minimize empirical expected loss of the pairwise intra-/inter- class proximity violations in the embedding space. We relate DML to feasibility problem of finite chance constraints. We show that minimizer…
Approaches to bivariate causal discovery based on the minimum description length (MDL) principle approximate the (uncomputable) Kolmogorov complexity of the models in each causal direction, selecting the one with the lower total complexity.…
Maximum pseudolikelihood (MPL) estimators are useful alternatives to maximum likelihood (ML) estimators when likelihood functions are more difficult to manipulate than their marginal and conditional components. Furthermore, MPL estimators…
Longitudinal Dispersion(LD) is the dominant process of scalar transport in natural streams. An accurate prediction on LD coefficient(Dl) can produce a performance leap in related simulation. The emerging machine learning(ML) techniques…
Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…
Consider the following prediction problem. Assume that there is a block box that produces bits according to some unknown computable distribution on the binary tree. We know first $n$ bits $x_1 x_2 \ldots x_n$. We want to know the…
Multi-distribution learning (MDL), which seeks to learn a shared model that minimizes the worst-case risk across $k$ distinct data distributions, has emerged as a unified framework in response to the evolving demand for robustness,…
The use of machine learning methods for predictive purposes has increased dramatically over the past two decades, but uncertainty quantification for predictive comparisons remains elusive. This paper addresses this gap by extending the…