arXiv research

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) variable ordering. The algorithm exhaustively searches through all network structures…

The minimum description length (MDL) principle in supervised learning is studied. One of the most important theories for the MDL principle is Barron and Cover's theory (BC theory), which gives a mathematical justification of the MDL principle. The original BC theory, however, can be applied to supervised learning only …

During the past few years Boolean matrix factorization (BMF) has become an important direction in data analysis. The minimum description length principle (MDL) was successfully adapted in BMF for the model order selection. Nevertheless, a BMF algorithm performing good results from the standpoint of standard measures in…

This document provides a tutorial description of the use of the MDL principle in complex graph analysis. We give a brief summary of the preliminary subjects, and describe the basic principle, using the example of analysing the size of the largest clique in a graph. We also provide a discussion of how to interpret the r…

MDL principle aids in learning neural network-based causal structures.

The Minimum Description Length (MDL) principle selects the model that has the shortest code for data plus model. We show that for a countable class of models, MDL predictions are close to the true distribution in a strong sense. The result is completely general. No independence, ergodicity, stationarity, identifiabilit…

We analyze differences between two information-theoretically motivated approaches to statistical inference and model selection: the Minimum Description Length (MDL) principle, and the Minimum Message Length (MML) principle. Based on this analysis, we present two revised versions of MML: a pointwise estimator which give…

Proposes a new method for two-dimensional data discretization.

A new complexity measure MDL-COMP for overparameterized models improves generalization performance.

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, the luckiness-normalized-maximum-likelihood(LNML)-minimization approach is favorab…

New model explains how concepts grow based on experience.

This is an up-to-date introduction to and overview of the Minimum Description Length (MDL) Principle, a theory of inductive inference that can be applied to general problems in statistics, machine learning and pattern recognition. While MDL was originally based on data compression ideas, this introduction can be read w…

The power of sparse signal modeling with learned over-complete dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical properties of these models, such as under-fitting or over-fitting given sets of data, …

Study improves neural network performance in sequential learning for image classification.

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 use standard conditional independence tests between the variables. To tackle this …

Proposes a new method for finding non-redundant, standout subgroups in numeric datasets.

New method improves bivariate causal discovery by accurately estimating cause variable complexity.

A new method identifies causal direction using dense functional classes.

Non-negative matrix factorization (NMF) is a dimensionality reduction technique which tends to produce a sparse representation of data. Commonly, the error between the actual and recreated matrices is used as an objective function, but this method may not produce the type of representation we desire as it allows for th…

Robust subgroup discovery finds non-redundant, statistically significant subgroups.

Given data over variables $(X_1,...,X_m, Y)$ we consider the problem of finding out whether $X$ jointly causes $Y$ or whether they are all confounded by an unobserved latent variable $Z$. To do so, we take an information-theoretic approach based on Kolmogorov complexity. In a nutshell, we follow the postulate that firs…

Interpretable classifiers have recently witnessed an increase in attention from the data mining community because they are inherently easier to understand and explain than their more complex counterparts. Examples of interpretable classification models include decision trees, rule sets, and rule lists. Learning such mo…

Fast, fully-automated histograms for large data sets.

We address the problem of adversarial examples in machine learning where an adversary tries to misguide a classifier by making functionality-preserving modifications to original samples. We assume a black-box scenario where the adversary has access to only the feature set, and the final hard-decision output of the clas…

New approach to learning kernels from data using AIT principles.

We design a classifier for transactional datasets with application in malware detection. We build the classifier based on the minimum description length (MDL) principle. This involves selecting a model that best compresses the training dataset for each class considering the MDL criterion. To select a model for a datase…

We analyze MDL for binary classification, quantifying overfitting and underfitting.

The parametric complexity is the key quantity in the minimum description length (MDL) approach to statistical model selection. Rissanen and others have shown that the parametric complexity of a statistical model approaches a simple function of the Fisher information volume of the model as the sample size $n$ goes to in…

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 describe the network, and avoid overfitting. According to this criterion, we obta…

This paper introduces a new notion of dimensionality of probabilistic models from an information-theoretic view point. We call it the "descriptive dimension"(Ddim). We show that Ddim coincides with the number of independent parameters for the parametric class, and can further be extended to real-valued dimensionality w…

In recent years there has been an increasing interest in learning Bayesian networks from data. One of the most effective methods for learning such networks is based on the minimum description length (MDL) principle. Previous work has shown that this learning procedure is asymptotically successful: with probability one,…

Paper proves convergence of MDL to Einstein-Hilbert with boundary term.

Study shows LLC correlates with neural network compressibility.

We introduce a deep, generative autoencoder capable of learning hierarchies of distributed representations from data. Successive deep stochastic hidden layers are equipped with autoregressive connections, which enable the model to be sampled from quickly and exactly via ancestral sampling. We derive an efficient approx…

Unified framework for PDF estimation using MDL-based binning and tensor factorization.

Proposes a method to adapt DNNs to drift in data distribution.

Given data over the joint distribution of two random variables $X$ and $Y$, we consider the problem of inferring the most likely causal direction between $X$ and $Y$. In particular, we consider the general case where both $X$ and $Y$ may be univariate or multivariate, and of the same or mixed data types. We take an inf…

In this paper we address the problem of discovering a small set of frequent serial episodes from sequential data so as to adequately characterize or summarize the data. We discuss an algorithm based on the Minimum Description Length (MDL) principle and the algorithm is a slight modification of an earlier method, called…

Generative model for creating graphs with new communities.

While statistics focusses on hypothesis testing and on estimating (properties of) the true sampling distribution, in machine learning the performance of learning algorithms on future data is the primary issue. In this paper we bridge the gap with a general principle (PHI) that identifies hypotheses with best predictive…

In this paper, we provide a new neural-network based perspective on multi-task learning (MTL) and multi-domain learning (MDL). By introducing the concept of a semantic descriptor, this framework unifies MDL and MTL as well as encompassing various classic and recent MTL/MDL algorithms by interpreting them as different w…

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 data models to recover the true underlying low-rank matrix when a large portion o…

The success of deep learning in numerous application domains created the de- sire to run and train them on mobile devices. This however, conflicts with their computationally, memory and energy intense nature, leading to a growing interest in compression. Recent work by Han et al. (2015a) propose a pipeline that involve…

The Minimum Description Length (MDL) principle states that the optimal model for a given data set is that which compresses it best. Due to practial limitations the model can be restricted to a class such as linear regression models, which we address in this study. As in other formulations such as the LASSO and forward …

Recent developments have linked causal inference with Algorithmic Information Theory, and methods have been developed that utilize Conditional Kolmogorov Complexity to determine causation between two random variables. We present a method for inferring causal direction between continuous variables by using an MDL Binnin…

Optimizes sample and round complexity in adaptive sampling from multiple distributions.

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 and estimation. Here we show that the normalized maximum likelihood has a Bayes-li…

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- of-sample predictive power and the latter possess easy interpretability. Recently,…