Independent from the still ongoing research in measuring individual intelligence, we anticipate and provide a framework for measuring collective intelligence. Collective intelligence refers to the idea that several individuals can collaborate in order to achieve high levels of intelligence. We present thus some ideas on how the intelligence of a group can be measured and simulate such tests. We will however focus here on groups of artificial intelligence agents (i.e., machines). We will explore how a group of agents is able to choose the appropriate problem and to specialize for a variety of tasks. This is a feature which is an important contributor to the increase of intelligence in a group (apart from the addition of more agents and the improvement due to common decision making). Our results reveal some interesting results about how (collective) intelligence can be modeled, about how collective intelligence tests can be designed and about the underlying dynamics of collective intelligence. As it will be useful for our simulations, we provide also some improvements of the threshold allocation model originally used in the area of swarm intelligence but further generalized here.

In the present paper we propose an unsupervised attribute ranking method based on evaluating the quality of clustering that each attribute produces by partitioning the data into subsets according to its values. We use the Minimum Description Length (MDL) principle to evaluate the quality of clustering and describe an algorithm for attribute ranking and a related clustering algorithm. Both algorithms are empirically evaluated on benchmark data sets. The experiments show that the MDL-based ranking performs closely to the supervised information gain ranking and thus improves the performance of the EM and k-means clustering algorithms in purely unsupervised setting.

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 obtain general bounds on the detectability of any prescribed block structure, given the number of nodes and edges in the sampled network. We also obtain that the maximum number of detectable blocks scales as $\sqrt{N}$, where $N$ is the number of nodes in the network, for a fixed average degree $$. We also show that the simplicity of the MDL approach yields an efficient multilevel Monte Carlo inference algorithm with a complexity of $O(\tau N\log N)$, if the number of blocks is unknown, and $O(\tau N)$ if it is known, where $\tau$ is the mixing time of the Markov chain. We illustrate the application of the method on a large network of actors and films with over $10^6$ edges, and a dissortative, bipartite block structure.

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 gives the MML-optimal single parameter model, and a volumewise estimator which gives the MML-optimal region in the parameter space. Our empirical results suggest that with small data sets, the MDL approach yields more accurate predictions than the MML estimators. The empirical results also demonstrate that the revised MML estimators introduced here perform better than the original MML estimator suggested by Wallace and Freeman.

The minimum message length(MML) principle[4] is an information theoretic criterion that links data compression with statistical inference [3]. It has a number of useful properties and it has close connections with Kolmogorov complexity [5]. Using the MML principle to construct estimators is known to be NPhard in general [1] so it is common to use approximations in practice [3]. The term'strict minimum message length' (SMML) is used to distinguish the exact MML criterion from these approximations. The only known algorithm for calculating an SMML estimator is Farr's algorithm [1] which applies to data taking values in a finite set which is (in some sense) 1-dimensional.

Recent developments in reinforcement learning for non-Markovianproblems witness a surge in history-based methods, among which weare particularly interested in two frameworks, PhiMDP and MC-AIXI-CTW. PhiMDP attempts to reduce the general RL problem, where the environment's states and dynamics are both unknown, toan MDP, while MC-AIXI-CTW incrementally learns a mixture of contexttrees as its environment model. The main idea of PhiMDP is toconnect generic reinforcement learning with classical reinforcementlearning. The first implementation of PhiMDP relies on astochastic search procedure for finding a tree that minimizes acertain cost function. This does not guarantee finding theminimizing tree, or even a good one, given limited search time. As aconsequence it appears that the approach has difficulties with largedomains. MC-AIXI-CTW is attractive in that it can incrementally andanalytically compute the internal model through interactions withthe environment. Unfortunately, it is computationally demanding dueto requiring heavy planning simulations at every single time step.We devise a novel approach called CTMRL, which analytically andefficiently finds the cost-minimizing tree. Instead of thecontext-tree weighting method that MC-AIXI-CTW is based on, we usethe closely related context-tree maximizing algorithm that selectsjust one single tree. This approach falls under the PhiMDPframework, which allows the replacement of the costly planningcomponent of MC-AIXI-CTW with simple Q-Learning. Our empiricalinvestigation show that CTMRL finds policies of quality as good as MC-AIXI-CTW's on sixdomains including a challenging Pacman domain, but in an order ofmagnitude less time.

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, are still not well characterized in the literature. As a result, the success of sparse modeling depends on hand-tuning critical parameters for each data and application. This work aims at addressing this by providing a practical and objective characterization of sparse models by means of the Minimum Description Length (MDL) principle -- a well established information-theoretic approach to model selection in statistical inference. The resulting framework derives a family of efficient sparse coding and dictionary learning algorithms which, by virtue of the MDL principle, are completely parameter free. Furthermore, such framework allows to incorporate additional prior information to existing models, such as Markovian dependencies, or to define completely new problem formulations, including in the matrix analysis area, in a natural way. These virtues will be demonstrated with parameter-free algorithms for the classic image denoising and classification problems, and for low-rank matrix recovery in video applications.

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 of the measured matrix is either missing or arbitrarily corrupted. However, if low rank is not a hypothesis about the true nature of the data, but a device for extracting regularity from it, no current guidelines exist for choosing the rank of the estimated matrix. In this work we address this problem by means of the Minimum Description Length (MDL) principle -- a well established information-theoretic approach to statistical inference -- as a guideline for selecting a model for the data at hand. We demonstrate the practical usefulness of our formal approach with results for complex background extraction in video sequences.

Faceted navigation can effectively reduce user efforts of reaching targeted resources in databases, by suggesting dynamic facet values for iterative query refinement. A key issue is minimizing the navigation cost in a user query session. Conventional navigation scheme assumes that at each step, users select only one suggested value to figure out resources containing it. To make faceted navigation more flexible and effective, this paper introduces a multi-select scheme where multiple suggested values can be selected at one step, and a selected value can be used to either retain or exclude the resources containing it. Previous algorithms for cost-driven value suggestion can hardly work well under our navigation scheme. Therefore, we propose to optimize the navigation cost using the Minimum Description Length principle, which can well balance the number of navigation steps and the number of suggested values per step under our new scheme. An emperical study demonstrates that our approach is more cost-saving and efficient than state-of-the-art approaches.

This book presents a methodology and philosophy of empirical science based on large scale lossless data compression. In this view a theory is scientific if it can be used to build a data compression program, and it is valuable if it can compress a standard benchmark database to a small size, taking into account the length of the compressor itself. This methodology therefore includes an Occam principle as well as a solution to the problem of demarcation. Because of the fundamental difficulty of lossless compression, this type of research must be empirical in nature: compression can only be achieved by discovering and characterizing empirical regularities in the data. Because of this, the philosophy provides a way to reformulate fields such as computer vision and computational linguistics as empirical sciences: the former by attempting to compress databases of natural images, the latter by attempting to compress large text databases. The book argues that the rigor and objectivity of the compression principle should set the stage for systematic progress in these fields. The argument is especially strong in the context of computer vision, which is plagued by chronic problems of evaluation. The book also considers the field of machine learning. Here the traditional approach requires that the models proposed to solve learning problems be extremely simple, in order to avoid overfitting. However, the world may contain intrinsically complex phenomena, which would require complex models to understand. The compression philosophy can justify complex models because of the large quantity of data being modeled (if the target database is 100 Gb, it is easy to justify a 10 Mb model). The complex models and abstractions learned on the basis of the raw data (images, language, etc) can then be reused to solve any specific learning problem, such as face recognition or machine translation.