Toshedlighton when change detection is easier than structured learning, we consider testing of edge deletion in forest-structured graphs, and high-temperature ferromagnets as casestudies.

We present novel information-theoretic limits on detecting sparse changes in Isingmodels, a problem that arises in many applications where network changes canoccur due to some external stimuli. We show that the sample complexity fordetecting sparse changes, in a minimax sense, is no better than learning the entiremodel even in settings with local sparsity. This is a surprising fact in light of priorwork rooted in sparse recovery methods, which suggest that sample complexityin this context scales only with the number of network changes. To shed light onwhen change detection is easier than structured learning, we consider testing ofedge deletion in forest-structured graphs, and high-temperature ferromagnets ascase studies. We show for these that testing of small changes is similarly hard, buttesting oflargechanges is well-separated from structure learning. These resultsimply that testing of graphical models may not be amenable to concepts such asrestricted strong convexity leveraged for sparsity pattern recovery, and algorithmdevelopment instead should be directed towards detection of large changes.

We present novel information-theoretic limits on detecting sparse changes in Ising models, a problem that arises in many applications where network changes can occur due to some external stimuli. We show that the sample complexity for detecting sparse changes, in a minimax sense, is no better than learning the entire model even in settings with local sparsity. This is a surprising fact in light of prior work rooted in sparse recovery methods, which suggest that sample complexity in this context scales only with the number of network changes. To shed light on when change detection is easier than structured learning, we consider testing of edge deletion in forest-structured graphs, and high-temperature ferromagnets as case studies. We show for these that testing of small changes is similarly hard, but testing of large changes is well-separated from structure learning. These results imply that testing of graphical models may not be amenable to concepts such as restricted strong convexity leveraged for sparsity pattern recovery, and algorithm development instead should be directed towards detection of large changes.

We present novel information-theoretic limits on detecting sparse changes in Isingmodels, a problem that arises in many applications where network changes canoccur due to some external stimuli. We show that the sample complexity fordetecting sparse changes, in a minimax sense, is no better than learning the entiremodel even in settings with local sparsity. This is a surprising fact in light of priorwork rooted in sparse recovery methods, which suggest that sample complexityin this context scales only with the number of network changes. To shed light onwhen change detection is easier than structured learning, we consider testing ofedge deletion in forest-structured graphs, and high-temperature ferromagnets ascase studies. We show for these that testing of small changes is similarly hard, buttesting oflargechanges is well-separated from structure learning.

We consider online change detection of high dimensional data streams with sparse changes, where only a subset of data streams can be observed at each sensing time point due to limited sensing capacities. On the one hand, the detection scheme should be able to deal with partially observable data and meanwhile have efficient detection power for sparse changes. On the other, the scheme should be able to adaptively and actively select the most important variables to observe to maximize the detection power. To address these two points, in this paper, we propose a novel detection scheme called CDSSD. In particular, it describes the structure of high dimensional data with sparse changes by smooth-sparse decomposition, whose parameters can be learned via spike-slab variational Bayesian inference. Then the posterior Bayes factor, which incorporates the learned parameters and sparse change information, is formulated as a detection statistic. Finally, by formulating the statistic as the reward of a combinatorial multi-armed bandit problem, an adaptive sampling strategy based on Thompson sampling is proposed. The efficacy and applicability of our method in practice are demonstrated with numerical studies and a real case study.

When applying principal component analysis (PCA) for dimension reduction, the most varying projections are usually used in order to retain most of the information. For the purpose of anomaly and change detection, however, the least varying projections are often the most important ones. In this article, we present a novel method that automatically tailors the choice of projections to monitor for sparse changes in the mean and/or covariance matrix of high-dimensional data. A subset of the least varying projections is almost always selected based on a criteria of the projection's sensitivity to changes. Our focus is on online/sequential change detection, where the aim is to detect changes as quickly as possible, while controlling false alarms at a specified level. A combination of tailored PCA and a generalized log-likelihood monitoring procedure displays high efficiency in detecting even very sparse changes in the mean, variance and correlation. We demonstrate on real data that tailored PCA monitoring is efficient for sparse change detection also when the data streams are highly auto-correlated and non-normal. Notably, error control is achieved without a large validation set, which is needed in most existing methods.

We study the problem of learning sparse structure changes between two Markov networks P and Q. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes directly via estimating the ratio between two Markov network models.  Such a direct approach was demonstrated to perform excellently in experiments, although its theoretical properties remained unexplored.  In this paper, we give sufficient conditions for successful change detection with respect to the sample size np, nq, the dimension of data m, and the number of changed edges d.

We propose a new method for detecting changes in Markov network structure between two sets of samples. Instead of naively fitting two Markov network models separately to the two data sets and figuring out their difference, we \emph{directly} learn the network structure change by estimating the ratio of Markov network models. This density-ratio formulation naturally allows us to introduce sparsity in the network structure change, which highly contributes to enhancing interpretability. Furthermore, computation of the normalization term, which is a critical bottleneck of the naive approach, can be remarkably mitigated. We also give the dual formulation of the optimization problem, which further reduces the computation cost for large-scale Markov networks. Through experiments, we demonstrate the usefulness of our method.