arXiv subjects

Kai Puolamäki

Publications and source records attributed to Kai Puolamäki.

29 records · Page 2Linked to original sources

arXiv2018

Human-Guided Data Exploration

The outcome of the explorative data analysis (EDA) phase is vital for successful data analysis. EDA is more effective when the user interacts with the system used to carry out the exploration. In the recently proposed paradigm of iterative data mining the user controls the exploration by inputting knowledge in the form of patterns observed during the process. The system then shows the user views of the data that are maximally informative given the user's current knowledge. Although this scheme is good at showing surprising views of the data to the user, there is a clear shortcoming: the user cannot steer the process. In many real cases we want to focus on investigating specific questions concerning the data. This paper presents the Human Guided Data Exploration framework, generalising previous research. This framework allows the user to incorporate existing knowledge into the exploration process, focus on exploring a subset of the data, and compare different complex hypotheses concerning relations in the data. The framework utilises a computationally efficient constrained randomisation scheme. To showcase the framework, we developed a free open-source tool, using which the empirical evaluation on real-world datasets was carried out. Our evaluation shows that the ability to focus on particular subsets and being able to compare hypotheses are important additions to the interactive iterative data mining process.

stat.ML↗

arXiv2017

Interactive Visual Data Exploration with Subjective Feedback: An Information-Theoretic Approach

Visual exploration of high-dimensional real-valued datasets is a fundamental task in exploratory data analysis (EDA). Existing methods use predefined criteria to choose the representation of data. There is a lack of methods that (i) elicit from the user what she has learned from the data and (ii) show patterns that she does not know yet. We construct a theoretical model where identified patterns can be input as knowledge to the system. The knowledge syntax here is intuitive, such as "this set of points forms a cluster", and requires no knowledge of maths. This background knowledge is used to find a Maximum Entropy distribution of the data, after which the system provides the user data projections in which the data and the Maximum Entropy distribution differ the most, hence showing the user aspects of the data that are maximally informative given the user's current knowledge. We provide an open source EDA system with tailored interactive visualizations to demonstrate these concepts. We study the performance of the system and present use cases on both synthetic and real data. We find that the model and the prototype system allow the user to learn information efficiently from various data sources and the system works sufficiently fast in practice. We conclude that the information theoretic approach to exploratory data analysis where patterns observed by a user are formalized as constraints provides a principled, intuitive, and efficient basis for constructing an EDA system.

stat.ML↗

arXiv2017

Subjectively Interesting Subgroup Discovery on Real-valued Targets

Deriving insights from high-dimensional data is one of the core problems in data mining. The difficulty mainly stems from the fact that there are exponentially many variable combinations to potentially consider, and there are infinitely many if we consider weighted combinations, even for linear combinations. Hence, an obvious question is whether we can automate the search for interesting patterns and visualizations. In this paper, we consider the setting where a user wants to learn as efficiently as possible about real-valued attributes. For example, to understand the distribution of crime rates in different geographic areas in terms of other (numerical, ordinal and/or categorical) variables that describe the areas. We introduce a method to find subgroups in the data that are maximally informative (in the formal Information Theoretic sense) with respect to a single or set of real-valued target attributes. The subgroup descriptions are in terms of a succinct set of arbitrarily-typed other attributes. The approach is based on the Subjective Interestingness framework FORSIED to enable the use of prior knowledge when finding most informative non-redundant patterns, and hence the method also supports iterative data mining.

stat.ML↗

arXiv2017

Interpreting Classifiers through Attribute Interactions in Datasets

In this work we present the novel ASTRID method for investigating which attribute interactions classifiers exploit when making predictions. Attribute interactions in classification tasks mean that two or more attributes together provide stronger evidence for a particular class label. Knowledge of such interactions makes models more interpretable by revealing associations between attributes. This has applications, e.g., in pharmacovigilance to identify interactions between drugs or in bioinformatics to investigate associations between single nucleotide polymorphisms. We also show how the found attribute partitioning is related to a factorisation of the data generating distribution and empirically demonstrate the utility of the proposed method.

stat.ML↗

arXiv2017

Finding Statistically Significant Attribute Interactions

In many data exploration tasks it is meaningful to identify groups of attribute interactions that are specific to a variable of interest. For instance, in a dataset where the attributes are medical markers and the variable of interest (class variable) is binary indicating presence/absence of disease, we would like to know which medical markers interact with respect to the binary class label. These interactions are useful in several practical applications, for example, to gain insight into the structure of the data, in feature selection, and in data anonymisation. We present a novel method, based on statistical significance testing, that can be used to verify if the data set has been created by a given factorised class-conditional joint distribution, where the distribution is parametrised by a partition of its attributes. Furthermore, we provide a method, named ASTRID, for automatically finding a partition of attributes describing the distribution that has generated the data. State-of-the-art classifiers are utilised to capture the interactions present in the data by systematically breaking attribute interactions and observing the effect of this breaking on classifier performance. We empirically demonstrate the utility of the proposed method with examples using real and synthetic data.

stat.ML↗

arXiv2017

Multivariate Confidence Intervals

Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying confidence intervals to multivariate data. In this paper we define confidence intervals for multivariate data that extend the one-dimensional definition in a natural way. In our definition every variable is associated with its own confidence interval as usual, but a data vector can be outside of a few of these, and still be considered to be within the confidence area. We analyze the problem and show that the resulting confidence areas retain the good qualities of their one-dimensional counterparts: they are informative and easy to interpret. Furthermore, we show that the problem of finding multivariate confidence intervals is hard, but provide efficient approximate algorithms to solve the problem.

stat.AP↗

arXiv2016

Clustering with Confidence: Finding Clusters with Statistical Guarantees

Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or re-running a clustering algorithm involving some stochastic component may lead to completely different clusters. There is, hence, a need for techniques that can quantify the instability of the generated clusters. In this study, we propose a technique for quantifying the instability of a clustering solution and for finding robust clusters, termed core clusters, which correspond to clusters where the co-occurrence probability of each data item within a cluster is at least $1 - α$. We demonstrate how solving the core clustering problem is linked to finding the largest maximal cliques in a graph. We show that the method can be used with both clustering and classification algorithms. The proposed method is tested on both simulated and real datasets. The results show that the obtained clusters indeed meet the guarantees on robustness.

stat.ML↗

arXiv2009

Multiple Hypothesis Testing in Pattern Discovery

The problem of multiple hypothesis testing arises when there are more than one hypothesis to be tested simultaneously for statistical significance. This is a very common situation in many data mining applications. For instance, assessing simultaneously the significance of all frequent itemsets of a single dataset entails a host of hypothesis, one for each itemset. A multiple hypothesis testing method is needed to control the number of false positives (Type I error). Our contribution in this paper is to extend the multiple hypothesis framework to be used with a generic data mining algorithm. We provide a method that provably controls the family-wise error rate (FWER, the probability of at least one false positive) in the strong sense. We evaluate the performance of our solution on both real and generated data. The results show that our method controls the FWER while maintaining the power of the test.

stat.ML↗

arXiv2008

Inference with Discriminative Posterior

We study Bayesian discriminative inference given a model family $p(c,\x, θ)$ that is assumed to contain all our prior information but still known to be incorrect. This falls in between "standard" Bayesian generative modeling and Bayesian regression, where the margin $p(\x,θ)$ is known to be uninformative about $p(c|\x,θ)$. We give an axiomatic proof that discriminative posterior is consistent for conditional inference; using the discriminative posterior is standard practice in classical Bayesian regression, but we show that it is theoretically justified for model families of joint densities as well. A practical benefit compared to Bayesian regression is that the standard methods of handling missing values in generative modeling can be extended into discriminative inference, which is useful if the amount of data is small. Compared to standard generative modeling, discriminative posterior results in better conditional inference if the model family is incorrect. If the model family contains also the true model, the discriminative posterior gives the same result as standard Bayesian generative modeling. Practical computation is done with Markov chain Monte Carlo.

stat.ML↗

arXiv2008

An Approximation Ratio for Biclustering

The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on the rows and on the columns of the input matrix. We show that such a solution yields a worst-case approximation ratio of 1+sqrt(2) under L1-norm for 0-1 valued matrices, and of 2 under L2-norm for real valued matrices.

cs.DS↗

arXiv1998

Critical basis dependence in bounding R-parity breaking couplings from neutral meson mixing

Assuming one nonzero product of two $λ'$-type couplings and working in two different bases for the left-handed quark superfields, the neutral meson mixings are used to bound these products. We emphasize the strong basis dependence of the bounds: in one basis many products contribute to neutral meson mixings at tree level, while in the other these products except one contribute at 1-loop level only and the GIM mechanism takes place. Correspondingly, these bounds differ between bases by orders of magnitudes.

hep-ph↗