44,183 research outputs found
Finding Statistically Significant Interactions between Continuous Features
The search for higher-order feature interactions that are statistically
significantly associated with a class variable is of high relevance in fields
such as Genetics or Healthcare, but the combinatorial explosion of the
candidate space makes this problem extremely challenging in terms of
computational efficiency and proper correction for multiple testing. While
recent progress has been made regarding this challenge for binary features, we
here present the first solution for continuous features. We propose an
algorithm which overcomes the combinatorial explosion of the search space of
higher-order interactions by deriving a lower bound on the p-value for each
interaction, which enables us to massively prune interactions that can never
reach significance and to thereby gain more statistical power. In our
experiments, our approach efficiently detects all significant interactions in a
variety of synthetic and real-world datasets.Comment: 13 pages, 5 figures, 2 tables, accepted to the 28th International
Joint Conference on Artificial Intelligence (IJCAI 2019
Mining Frequent Graph Patterns with Differential Privacy
Discovering frequent graph patterns in a graph database offers valuable
information in a variety of applications. However, if the graph dataset
contains sensitive data of individuals such as mobile phone-call graphs and
web-click graphs, releasing discovered frequent patterns may present a threat
to the privacy of individuals. {\em Differential privacy} has recently emerged
as the {\em de facto} standard for private data analysis due to its provable
privacy guarantee. In this paper we propose the first differentially private
algorithm for mining frequent graph patterns.
We first show that previous techniques on differentially private discovery of
frequent {\em itemsets} cannot apply in mining frequent graph patterns due to
the inherent complexity of handling structural information in graphs. We then
address this challenge by proposing a Markov Chain Monte Carlo (MCMC) sampling
based algorithm. Unlike previous work on frequent itemset mining, our
techniques do not rely on the output of a non-private mining algorithm.
Instead, we observe that both frequent graph pattern mining and the guarantee
of differential privacy can be unified into an MCMC sampling framework. In
addition, we establish the privacy and utility guarantee of our algorithm and
propose an efficient neighboring pattern counting technique as well.
Experimental results show that the proposed algorithm is able to output
frequent patterns with good precision
Sparse Learning over Infinite Subgraph Features
We present a supervised-learning algorithm from graph data (a set of graphs)
for arbitrary twice-differentiable loss functions and sparse linear models over
all possible subgraph features. To date, it has been shown that under all
possible subgraph features, several types of sparse learning, such as Adaboost,
LPBoost, LARS/LASSO, and sparse PLS regression, can be performed. Particularly
emphasis is placed on simultaneous learning of relevant features from an
infinite set of candidates. We first generalize techniques used in all these
preceding studies to derive an unifying bounding technique for arbitrary
separable functions. We then carefully use this bounding to make block
coordinate gradient descent feasible over infinite subgraph features, resulting
in a fast converging algorithm that can solve a wider class of sparse learning
problems over graph data. We also empirically study the differences from the
existing approaches in convergence property, selected subgraph features, and
search-space sizes. We further discuss several unnoticed issues in sparse
learning over all possible subgraph features.Comment: 42 pages, 24 figures, 4 table
Finding the True Frequent Itemsets
Frequent Itemsets (FIs) mining is a fundamental primitive in data mining. It
requires to identify all itemsets appearing in at least a fraction of
a transactional dataset . Often though, the ultimate goal of
mining is not an analysis of the dataset \emph{per se}, but the
understanding of the underlying process that generated it. Specifically, in
many applications is a collection of samples obtained from an
unknown probability distribution on transactions, and by extracting the
FIs in one attempts to infer itemsets that are frequently (i.e.,
with probability at least ) generated by , which we call the True
Frequent Itemsets (TFIs). Due to the inherently stochastic nature of the
generative process, the set of FIs is only a rough approximation of the set of
TFIs, as it often contains a huge number of \emph{false positives}, i.e.,
spurious itemsets that are not among the TFIs. In this work we design and
analyze an algorithm to identify a threshold such that the
collection of itemsets with frequency at least in
contains only TFIs with probability at least , for some
user-specified . Our method uses results from statistical learning
theory involving the (empirical) VC-dimension of the problem at hand. This
allows us to identify almost all the TFIs without including any false positive.
We also experimentally compare our method with the direct mining of
at frequency and with techniques based on widely-used
standard bounds (i.e., the Chernoff bounds) of the binomial distribution, and
show that our algorithm outperforms these methods and achieves even better
results than what is guaranteed by the theoretical analysis.Comment: 13 pages, Extended version of work appeared in SIAM International
Conference on Data Mining, 201
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