During the past few years Boolean matrix factorization (BMF) has become an important direction in data analysis. The minimum description length principle (MDL) was successfully adapted in BMF for the model order selection. Nevertheless, a BMF algorithm performing good results from the standpoint of standard measures in BMF is missing. In this paper, we propose a novel from-below Boolean matrix factorization algorithm based on formal concept analysis. The algorithm utilizes the MDL principle as a criterion for the factor selection. On various experiments we show that the proposed algorithm outperforms---from different standpoints---existing state-of-the-art BMF algorithms.

Anomaly detecting as an important technical in cloud computing is applied to support smooth running of the cloud platform. Traditional detecting methods based on statistic, analysis, etc. lead to the high false-alarm rate due to non-adaptive and sensitive parameters setting. We presented an online model for anomaly detecting using machine learning theory. However, most existing methods based on machine learning linked all features from difference sub-systems into a long feature vector directly, which is difficult to both exploit the complement information between sub-systems and ignore multi-view features enhancing the classification performance. Aiming to this problem, the proposed method automatic fuses multi-view features and optimize the discriminative model to enhance the accuracy. This model takes advantage of extreme learning machine (ELM) to improve detection efficiency. ELM is the single hidden layer neural network, which is transforming iterative solution the output weights to solution of linear equations and avoiding the local optimal solution. Moreover, we rank anomies according to the relationship between samples and the classification boundary, and then assigning weights for ranked anomalies, retraining the classification model finally. Our method exploits the complement information between sub-systems sufficiently, and avoids the influence from imbalance dataset, therefore, deal with various challenges from the cloud computing platform. We deploy the privately cloud platform by Openstack, verifying the proposed model and comparing results to the state-of-the-art methods with better efficiency and simplicity.

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.

In this work, we introduce the concept of bandlimiting into the theory of machine learning because all physical processes are bandlimited by nature, including real-world machine learning tasks. After the bandlimiting constraint is taken into account, our theoretical analysis has shown that all practical machine learning tasks are asymptotically solvable in a perfect sense. Furthermore, the key towards this solvability almost solely relies on two factors: i) a sufficiently large amount of training samples beyond a threshold determined by a difficulty measurement of the underlying task; ii) a sufficiently complex model that is properly bandlimited. Moreover, for some special cases, we have derived new error bounds for perfect learning, which can quantify the difficulty of learning. These case-specific bounds are much tighter than the uniform bounds in conventional learning theory. Our results have provided a new perspective to explain the recent successes of large-scale supervised learning using complex models like neural networks.

We consider the minimum cost intervention design problem: Given the essential graph of a causal graph and a cost to intervene on a variable, identify the set of interventions with minimum total cost that can learn any causal graph with the given essential graph. We first show that this problem is NP-hard. We then prove that we can achieve a constant factor approximation to this problem with a greedy algorithm. We then constrain the sparsity of each intervention. We develop an algorithm that returns an intervention design that is nearly optimal in terms of size for sparse graphs with sparse interventions and we discuss how to use it when there are costs on the vertices.

Bounding the generalization error of learning algorithms has a long history, which yet falls short in explaining various generalization successes including those of deep learning. Two important difficulties are (i) exploiting the dependencies between the hypotheses, (ii) exploiting the dependence between the algorithm's input and output. Progress on the first point was made with the chaining method, originating from the work of Kolmogorov, and used in the VC-dimension bound. More recently, progress on the second point was made with the mutual information method by Russo and Zou '15. Yet, these two methods are currently disjoint. In this paper, we introduce a technique to combine the chaining and mutual information methods, to obtain a generalization bound that is both algorithm-dependent and that exploits the dependencies between the hypotheses. We provide an example in which our bound significantly outperforms both the chaining and the mutual information bounds. As a corollary, we tighten Dudley's inequality when the learning algorithm chooses its output from a small subset of hypotheses with high probability.

We study a recent model of collaborative PAC learning where $k$ players with $k$ different tasks collaborate to learn a single classifier that works for all tasks. Previous work showed that when there is a classifier that has very small error on all tasks, there is a collaborative algorithm that finds a single classifier for all tasks and has $O((\ln (k))^2)$ times the worst-case sample complexity for learning a single task. In this work, we design new algorithms for both the realizable and the non-realizable setting, having sample complexity only $O(\ln (k))$ times the worst-case sample complexity for learning a single task. The sample complexity upper bounds of our algorithms match previous lower bounds and in some range of parameters are even better than previous algorithms that are allowed to output different classifiers for different tasks.

The existence of evasion attacks during the test phase of machine learning algorithms represents a significant challenge to both their deployment and understanding. These attacks can be carried out by adding imperceptible perturbations to inputs to generate adversarial examples and finding effective defenses and detectors has proven to be difficult. In this paper, we step away from the attack-defense arms race and seek to understand the limits of what can be learned in the presence of an evasion adversary. In particular, we extend the Probably Approximately Correct (PAC)-learning framework to account for the presence of an adversary. We first define corrupted hypothesis classes which arise from standard binary hypothesis classes in the presence of an evasion adversary and derive the Vapnik-Chervonenkis (VC)-dimension for these, denoted as the adversarial VC-dimension. We then show that sample complexity upper bounds from the Fundamental Theorem of Statistical learning can be extended to the case of evasion adversaries, where the sample complexity is controlled by the adversarial VC-dimension. We then explicitly derive the adversarial VC-dimension for halfspace classifiers in the presence of a sample-wise norm-constrained adversary of the type commonly studied for evasion attacks and show that it is the same as the standard VC-dimension, closing an open question. Finally, we prove that the adversarial VC-dimension can be either larger or smaller than the standard VC-dimension depending on the hypothesis class and adversary, making it an interesting object of study in its own right.

We consider the minimum cost intervention design problem: Given the essential graph of a causal graph and a cost to intervene on a variable, identify the set of interventions with minimum total cost that can learn any causal graph with the given essential graph. We first show that this problem is NP-hard. We then prove that we can achieve a constant factor approximation to this problem with a greedy algorithm. We then constrain the sparsity of each intervention. We develop an algorithm that returns an intervention design that is nearly optimal in terms of size for sparse graphs with sparse interventions and we discuss how to use it when there are costs on the vertices.

We study robust subspace estimation in the streaming and distributed settings. Given a set of n data points {a_i}_{i=1}^n in R^d and an integer k, we wish to find a linear subspace S of dimension k for which sum_i M(dist(S, a_i)) is minimized, where dist(S,x) := min_{y in S} |x-y|_2, and M() is some loss function. When M is the identity function, S gives a subspace that is more robust to outliers than that provided by the truncated SVD. Though the problem is NP-hard, it is approximable within a (1+epsilon) factor in polynomial time when k and epsilon are constant. We give the first sublinear approximation algorithm for this problem in the turnstile streaming and arbitrary partition distributed models, achieving the same time guarantees as in the offline case. Our algorithm is the first based entirely on oblivious dimensionality reduction, and significantly simplifies prior methods for this problem, which held in neither the streaming nor distributed models.