arXiv subjects

Jilles Vreeken

Publications and source records attributed to Jilles Vreeken.

At least 55 records · Page 3Linked to original sources

arXiv2019

Summarizing Data Succinctly with the Most Informative Itemsets

Knowledge discovery from data is an inherently iterative process. That is, what we know about the data greatly determines our expectations, and therefore, what results we would find interesting and/or surprising. Given new knowledge about the data, our expectations will change. Hence, in order to avoid redundant results, knowledge discovery algorithms ideally should follow such an iterative updating procedure. With this in mind, we introduce a well-founded approach for succinctly summarizing data with the most informative itemsets; using a probabilistic maximum entropy model, we iteratively find the itemset that provides us the most novel information--that is, for which the frequency in the data surprises us the most---and in turn we update our model accordingly. As we use the Maximum Entropy principle to obtain unbiased probabilistic models, and only include those itemsets that are most informative with regard to the current model, the summaries we construct are guaranteed to be both descriptive and non-redundant. The algorithm that we present, called MTV, can either discover the top-$k$ most informative itemsets, or we can employ either the Bayesian Information Criterion (BIC) or the Minimum Description Length (MDL) principle to automatically identify the set of itemsets that together summarize the data well. In other words, our method will `tell you what you need to know' about the data. Importantly, it is a one-phase algorithm: rather than picking itemsets from a user-provided candidate set, itemsets and their supports are mined on-the-fly. To further its applicability, we provide an efficient method to compute the maximum entropy distribution using Quick Inclusion-Exclusion. Experiments on our method, using synthetic, benchmark, and real data, show that the discovered summaries are succinct, and correctly identify the key patterns in the data.

cs.DS↗

arXiv2019

Comparing Apples and Oranges: Measuring Differences between Exploratory Data Mining Results

Deciding whether the results of two different mining algorithms provide significantly different information is an important, yet understudied, open problem in exploratory data mining. Whether the goal is to select the most informative result for analysis, or to decide which mining approach will most likely provide the most novel insight, it is essential that we can tell how different the information is that different results by possibly different methods provide. In this paper we take a first step towards comparing exploratory data mining results on binary data. We propose to meaningfully convert results into sets of noisy tiles, and compare between these sets by Maximum Entropy modelling and Kullback-Leibler divergence, well-founded notions from Information Theory. We so construct a measure that is highly flexible, and allows us to naturally include background knowledge, such that differences in results can be measured from the perspective of what a user already knows. Furthermore, adding to its interpretability, it coincides with Jaccard dissimilarity when we only consider exact tiles. Our approach provides a means to study and tell differences between results of different exploratory data mining methods. As an application, we show that our measure can also be used to identify which parts of results best redescribe other results. Furthermore, we study its use for iterative data mining, where one iteratively wants to find that result that will provide maximal novel information. Experimental evaluation shows our measure gives meaningful results, correctly identifies methods that are similar in nature, automatically provides sound redescriptions of results, and is highly applicable for iterative data mining.

cs.DB↗

arXiv2019

Testing Conditional Independence on Discrete Data using Stochastic Complexity

Testing for conditional independence is a core aspect of constraint-based causal discovery. Although commonly used tests are perfect in theory, they often fail to reject independence in practice, especially when conditioning on multiple variables. We focus on discrete data and propose a new test based on the notion of algorithmic independence that we instantiate using stochastic complexity. Amongst others, we show that our proposed test, SCI, is an asymptotically unbiased as well as $L_2$ consistent estimator for conditional mutual information (CMI). Further, we show that SCI can be reformulated to find a sensible threshold for CMI that works well on limited samples. Empirical evaluation shows that SCI has a lower type II error than commonly used tests. As a result, we obtain a higher recall when we use SCI in causal discovery algorithms, without compromising the precision.

stat.ML↗

arXiv2019

Discovering Descriptive Tile Trees by Mining Optimal Geometric Subtiles

When analysing binary data, the ease at which one can interpret results is very important. Many existing methods, however, discover either models that are difficult to read, or return so many results interpretation becomes impossible. Here, we study a fully automated approach for mining easily interpretable models for binary data. We model data hierarchically with noisy tiles-rectangles with significantly different density than their parent tile. To identify good trees, we employ the Minimum Description Length principle. We propose STIJL, a greedy any-time algorithm for mining good tile trees from binary data. Iteratively, it finds the locally optimal addition to the current tree, allowing overlap with tiles of the same parent. A major result of this paper is that we find the optimal tile in only $Θ(NM\min(N, M))$ time. STIJL can either be employed as a top-$k$ miner, or by MDL we can identify the tree that describes the data best. Experiments show we find succinct models that accurately summarise the data, and, by their hierarchical property are easily interpretable.

cs.DS↗

arXiv2019

The Long and the Short of It: Summarising Event Sequences with Serial Episodes

An ideal outcome of pattern mining is a small set of informative patterns, containing no redundancy or noise, that identifies the key structure of the data at hand. Standard frequent pattern miners do not achieve this goal, as due to the pattern explosion typically very large numbers of highly redundant patterns are returned. We pursue the ideal for sequential data, by employing a pattern set mining approach-an approach where, instead of ranking patterns individually, we consider results as a whole. Pattern set mining has been successfully applied to transactional data, but has been surprisingly under studied for sequential data. In this paper, we employ the MDL principle to identify the set of sequential patterns that summarises the data best. In particular, we formalise how to encode sequential data using sets of serial episodes, and use the encoded length as a quality score. As search strategy, we propose two approaches: the first algorithm selects a good pattern set from a large candidate set, while the second is a parameter-free any-time algorithm that mines pattern sets directly from the data. Experimentation on synthetic and real data demonstrates we efficiently discover small sets of informative patterns.

cs.DS↗

arXiv2019

Finding Good Itemsets by Packing Data

The problem of selecting small groups of itemsets that represent the data well has recently gained a lot of attention. We approach the problem by searching for the itemsets that compress the data efficiently. As a compression technique we use decision trees combined with a refined version of MDL. More formally, assuming that the items are ordered, we create a decision tree for each item that may only depend on the previous items. Our approach allows us to find complex interactions between the attributes, not just co-occurrences of 1s. Further, we present a link between the itemsets and the decision trees and use this link to export the itemsets from the decision trees. In this paper we present two algorithms. The first one is a simple greedy approach that builds a family of itemsets directly from data. The second one, given a collection of candidate itemsets, selects a small subset of these itemsets. Our experiments show that these approaches result in compact and high quality descriptions of the data.

cs.DS↗

arXiv2019

We Are Not Your Real Parents: Telling Causal from Confounded using MDL

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 first encoding the true cause, and then the effects given that cause, results in a shorter description than any other encoding of the observed variables. The ideal score is not computable, and hence we have to approximate it. We propose to do so using the Minimum Description Length (MDL) principle. We compare the MDL scores under the models where $X$ causes $Y$ and where there exists a latent variables $Z$ confounding both $X$ and $Y$ and show our scores are consistent. To find potential confounders we propose using latent factor modeling, in particular, probabilistic PCA (PPCA). Empirical evaluation on both synthetic and real-world data shows that our method, CoCa, performs very well -- even when the true generating process of the data is far from the assumptions made by the models we use. Moreover, it is robust as its accuracy goes hand in hand with its confidence.

cs.LG↗

arXiv2018

Discovering Reliable Dependencies from Data: Hardness and Improved Algorithms

The reliable fraction of information is an attractive score for quantifying (functional) dependencies in high-dimensional data. In this paper, we systematically explore the algorithmic implications of using this measure for optimization. We show that the problem is NP-hard, which justifies the usage of worst-case exponential-time as well as heuristic search methods. We then substantially improve the practical performance for both optimization styles by deriving a novel admissible bounding function that has an unbounded potential for additional pruning over the previously proposed one. Finally, we empirically investigate the approximation ratio of the greedy algorithm and show that it produces highly competitive results in a fraction of time needed for complete branch-and-bound style search.

cs.AI↗

arXiv2018

Causal Discovery by Telling Apart Parents and Children

We consider the problem of inferring the directed, causal graph from observational data, assuming no hidden confounders. We take an information theoretic approach, and make three main contributions. First, we show how through algorithmic information theory we can obtain SCI, a highly robust, effective and computationally efficient test for conditional independence---and show it outperforms the state of the art when applied in constraint-based inference methods such as stable PC. Second, building upon on SCI, we show how to tell apart the parents and children of a given node based on the algorithmic Markov condition. We give the Climb algorithm to efficiently discover the directed, causal Markov blanket---and show it is at least as accurate as inferring the global network, while being much more efficient. Last, but not least, we detail how we can use the Climb score to direct those edges that state of the art causal discovery algorithms based on PC or GES leave undirected---and show this improves their precision, recall and F1 scores by up to 20%.

stat.ML↗

arXiv2017

Causal Inference on Multivariate and Mixed-Type Data

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 information theoretic approach, based on Kolmogorov complexity, from which it follows that first describing the data over cause and then that of effect given cause is shorter than the reverse direction. The ideal score is not computable, but can be approximated through the Minimum Description Length (MDL) principle. Based on MDL, we propose two scores, one for when both $X$ and $Y$ are of the same single data type, and one for when they are mixed-type. We model dependencies between $X$ and $Y$ using classification and regression trees. As inferring the optimal model is NP-hard, we propose Crack, a fast greedy algorithm to determine the most likely causal direction directly from the data. Empirical evaluation on a wide range of data shows that Crack reliably, and with high accuracy, infers the correct causal direction on both univariate and multivariate cause-effect pairs over both single and mixed-type data.

stat.ML↗

arXiv2017

Telling Cause from Effect using MDL-based Local and Global Regression

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 problem, we follow an information theoretic approach based on Kolmogorov complexity and use the Minimum Description Length (MDL) principle to provide a practical solution. In particular, we propose a compression scheme to encode local and global functional relations using MDL-based regression. We infer $X$ causes $Y$ in case it is shorter to describe $Y$ as a function of $X$ than the inverse direction. In addition, we introduce Slope, an efficient linear-time algorithm that through thorough empirical evaluation on both synthetic and real world data we show outperforms the state of the art by a wide margin.

stat.ML↗

arXiv2017

Efficiently Discovering Locally Exceptional yet Globally Representative Subgroups

Subgroup discovery is a local pattern mining technique to find interpretable descriptions of sub-populations that stand out on a given target variable. That is, these sub-populations are exceptional with regard to the global distribution. In this paper we argue that in many applications, such as scientific discovery, subgroups are only useful if they are additionally representative of the global distribution with regard to a control variable. That is, when the distribution of this control variable is the same, or almost the same, as over the whole data. We formalise this objective function and give an efficient algorithm to compute its tight optimistic estimator for the case of a numeric target and a binary control variable. This enables us to use the branch-and-bound framework to efficiently discover the top-$k$ subgroups that are both exceptional as well as representative. Experimental evaluation on a wide range of datasets shows that with this algorithm we discover meaningful representative patterns and are up to orders of magnitude faster in terms of node evaluations as well as time.

cs.DB↗

arXiv2017

Discovering Reliable Approximate Functional Dependencies

Given a database and a target attribute of interest, how can we tell whether there exists a functional, or approximately functional dependence of the target on any set of other attributes in the data? How can we reliably, without bias to sample size or dimensionality, measure the strength of such a dependence? And, how can we efficiently discover the optimal or $α$-approximate top-$k$ dependencies? These are exactly the questions we answer in this paper. As we want to be agnostic on the form of the dependence, we adopt an information-theoretic approach, and construct a reliable, bias correcting score that can be efficiently computed. Moreover, we give an effective optimistic estimator of this score, by which for the first time we can mine the approximate functional dependencies from data with guarantees of optimality. Empirical evaluation shows that the derived score achieves a good bias for variance trade-off, can be used within an efficient discovery algorithm, and indeed discovers meaningful dependencies. Most important, it remains reliable in the face of data sparsity.

cs.DB↗

arXiv2017

Identifying Consistent Statements about Numerical Data with Dispersion-Corrected Subgroup Discovery

Existing algorithms for subgroup discovery with numerical targets do not optimize the error or target variable dispersion of the groups they find. This often leads to unreliable or inconsistent statements about the data, rendering practical applications, especially in scientific domains, futile. Therefore, we here extend the optimistic estimator framework for optimal subgroup discovery to a new class of objective functions: we show how tight estimators can be computed efficiently for all functions that are determined by subgroup size (non-decreasing dependence), the subgroup median value, and a dispersion measure around the median (non-increasing dependence). In the important special case when dispersion is measured using the average absolute deviation from the median, this novel approach yields a linear time algorithm. Empirical evaluation on a wide range of datasets shows that, when used within branch-and-bound search, this approach is highly efficient and indeed discovers subgroups with much smaller errors.

cs.AI↗

arXiv2017

Causal Inference by Stochastic Complexity

The algorithmic Markov condition states that the most likely causal direction between two random variables X and Y can be identified as that direction with the lowest Kolmogorov complexity. Due to the halting problem, however, this notion is not computable. We hence propose to do causal inference by stochastic complexity. That is, we propose to approximate Kolmogorov complexity via the Minimum Description Length (MDL) principle, using a score that is mini-max optimal with regard to the model class under consideration. This means that even in an adversarial setting, such as when the true distribution is not in this class, we still obtain the optimal encoding for the data relative to the class. We instantiate this framework, which we call CISC, for pairs of univariate discrete variables, using the class of multinomial distributions. Experiments show that CISC is highly accurate on synthetic, benchmark, as well as real-world data, outperforming the state of the art by a margin, and scales extremely well with regard to sample and domain sizes.

cs.LG↗

arXiv2017

Efficiently Summarising Event Sequences with Rich Interleaving Patterns

Discovering the key structure of a database is one of the main goals of data mining. In pattern set mining we do so by discovering a small set of patterns that together describe the data well. The richer the class of patterns we consider, and the more powerful our description language, the better we will be able to summarise the data. In this paper we propose \ourmethod, a novel greedy MDL-based method for summarising sequential data using rich patterns that are allowed to interleave. Experiments show \ourmethod is orders of magnitude faster than the state of the art, results in better models, as well as discovers meaningful semantics in the form patterns that identify multiple choices of values.

cs.AI↗

arXiv2016

Interactive and Iterative Discovery of Entity Network Subgraphs

Graph mining to extract interesting components has been studied in various guises, e.g., communities, dense subgraphs, cliques. However, most existing works are based on notions of frequency and connectivity and do not capture subjective interestingness from a user's viewpoint. Furthermore, existing approaches to mine graphs are not interactive and cannot incorporate user feedbacks in any natural manner. In this paper, we address these gaps by proposing a graph maximum entropy model to discover surprising connected subgraph patterns from entity graphs. This model is embedded in an interactive visualization framework to enable human-in-the-loop, model-guided data exploration. Using case studies on real datasets, we demonstrate how interactions between users and the maximum entropy model lead to faster and explainable conclusions.

cs.SI↗

arXiv2016

Seeing the Forest through the Trees: Adaptive Local Exploration of Large Graphs

Visualization is a powerful paradigm for exploratory data analysis. Visualizing large graphs, however, often results in a meaningless hairball. In this paper, we propose a different approach that helps the user adaptively explore large million-node graphs from a local perspective. For nodes that the user investigates, we propose to only show the neighbors with the most subjectively interesting neighborhoods. We contribute novel ideas to measure this interestingness in terms of how surprising a neighborhood is given the background distribution, as well as how well it fits the nodes the user chose to explore. We introduce FACETS, a fast and scalable method for visually exploring large graphs. By implementing our above ideas, it allows users to look into the forest through its trees. Empirical evaluation shows that our method works very well in practice, providing rankings of nodes that match interests of users. Moreover, as it scales linearly, FACETS is suited for the exploration of very large graphs.

cs.IR↗