Recent research on deep neural networks has focused primarily on improving accuracy. For a given accuracy level, it is typically possible to identify multiple DNN architectures that achieve that accuracy level. With equivalent accuracy, smaller DNN architectures offer at least three advantages: (1) Smaller DNNs require less communication across servers during distributed training. (2) Smaller DNNs require less bandwidth to export a new model from the cloud to an autonomous car. (3) Smaller DNNs are more feasible to deploy on FPGAs and other hardware with limited memory. To provide all of these advantages, we propose a small DNN architecture called SqueezeNet. SqueezeNet achieves AlexNet-level accuracy on ImageNet with 50x fewer parameters. Additionally, with model compression techniques we are able to compress SqueezeNet to less than 0.5MB (510x smaller than AlexNet). The SqueezeNet architecture is available for download here: https://github.com/DeepScale/SqueezeNet

We consider the problem of estimating the class prior in an unlabeled dataset. Under the assumption that an additional labeled dataset is available, the class prior can be estimated by fitting a mixture of class-wise data distributions to the unlabeled data distribution. However, in practice, such an additional labeled dataset is often not available. In this paper, we show that, with additional samples coming only from the positive class, the class prior of the unlabeled dataset can be estimated correctly. Our key idea is to use properly penalized divergences for model fitting to cancel the error caused by the absence of negative samples. We further show that the use of the penalized $L_1$-distance gives a computationally efficient algorithm with an analytic solution. The consistency, stability, and estimation error are theoretically analyzed. Finally, we experimentally demonstrate the usefulness of the proposed method.

We propose a method to classify the causal relationship between two discrete variables given only the joint distribution of the variables, acknowledging that the method is subject to an inherent baseline error. We assume that the causal system is acyclicity, but we do allow for hidden common causes. Our algorithm presupposes that the probability distributions $P(C)$ of a cause $C$ is independent from the probability distribution $P(E\mid C)$ of the cause-effect mechanism. While our classifier is trained with a Bayesian assumption of flat hyperpriors, we do not make this assumption about our test data. This work connects to recent developments on the identifiability of causal models over continuous variables under the assumption of "independent mechanisms". Carefully-commented Python notebooks that reproduce all our experiments are available online at http://vision.caltech.edu/~kchalupk/code.html.

Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or pre-determined sensing arrangements, like in road transportation networks for example. In general though, the data structure is not readily available and becomes pretty difficult to define. In particular, the global smoothness assumptions, that most of the existing works adopt, are often too general and unable to properly capture localized properties of data. In this paper, we go beyond this classical data model and rather propose to represent information as a sparse combination of localized functions that live on a data structure represented by a graph. Based on this model, we focus on the problem of inferring the connectivity that best explains the data samples at different vertices of a graph that is a priori unknown. We concentrate on the case where the observed data is actually the sum of heat diffusion processes, which is a quite common model for data on networks or other irregular structures. We cast a new graph learning problem and solve it with an efficient nonconvex optimization algorithm. Experiments on both synthetic and real world data finally illustrate the benefits of the proposed graph learning framework and confirm that the data structure can be efficiently learned from data observations only. We believe that our algorithm will help solving key questions in diverse application domains such as social and biological network analysis where it is crucial to unveil proper geometry for data understanding and inference.

The GANs are generative models whose random samples realistically reflect natural images. It also can generate samples with specific attributes by concatenating a condition vector into the input, yet research on this field is not well studied. We propose novel methods of conditioning generative adversarial networks (GANs) that achieve state-of-the-art results on MNIST and CIFAR-10. We mainly introduce two models: an information retrieving model that extracts conditional information from the samples, and a spatial bilinear pooling model that forms bilinear features derived from the spatial cross product of an image and a condition vector. These methods significantly enhance log-likelihood of test data under the conditional distributions compared to the methods of concatenation.

We focus in this work on the estimation of the first $k$ eigenvectors of any graph Laplacian using filtering of Gaussian random signals. We prove that we only need $k$ such signals to be able to exactly recover as many of the smallest eigenvectors, regardless of the number of nodes in the graph. In addition, we address key issues in implementing the theoretical concepts in practice using accurate approximated methods. We also propose fast algorithms both for eigenspace approximation and for the determination of the $k$th smallest eigenvalue $\lambda_k$. The latter proves to be extremely efficient under the assumption of locally uniform distribution of the eigenvalue over the spectrum. Finally, we present experiments which show the validity of our method in practice and compare it to state-of-the-art methods for clustering and visualization both on synthetic small-scale datasets and larger real-world problems of millions of nodes. We show that our method allows a better scaling with the number of nodes than all previous methods while achieving an almost perfect reconstruction of the eigenspace formed by the first $k$ eigenvectors.

We investigate the problem of testing whether $d$ random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two variable Hilbert-Schmidt independence criterion (HSIC) but allows for an arbitrary number of variables. We embed the $d$-dimensional joint distribution and the product of the marginals into a reproducing kernel Hilbert space and define the $d$-variable Hilbert-Schmidt independence criterion (dHSIC) as the squared distance between the embeddings. In the population case, the value of dHSIC is zero if and only if the $d$ variables are jointly independent, as long as the kernel is characteristic. Based on an empirical estimate of dHSIC, we define three different non-parametric hypothesis tests: a permutation test, a bootstrap test and a test based on a Gamma approximation. We prove that the permutation test achieves the significance level and that the bootstrap test achieves pointwise asymptotic significance level as well as pointwise asymptotic consistency (i.e., it is able to detect any type of fixed dependence in the large sample limit). The Gamma approximation does not come with these guarantees; however, it is computationally very fast and for small $d$, it performs well in practice. Finally, we apply the test to a problem in causal discovery.

The amount of data available in the world is growing faster than our ability to deal with it. However, if we take advantage of the internal \emph{structure}, data may become much smaller for machine learning purposes. In this paper we focus on one of the fundamental machine learning tasks, empirical risk minimization (ERM), and provide faster algorithms with the help from the clustering structure of the data. We introduce a simple notion of raw clustering that can be efficiently computed from the data, and propose two algorithms based on clustering information. Our accelerated algorithm ClusterACDM is built on a novel Haar transformation applied to the dual space of the ERM problem, and our variance-reduction based algorithm ClusterSVRG introduces a new gradient estimator using clustering. Our algorithms outperform their classical counterparts ACDM and SVRG respectively.

Attack graphs are a powerful tool for security risk assessment by analysing network vulnerabilities and the paths attackers can use to compromise network resources. The uncertainty about the attacker's behaviour makes Bayesian networks suitable to model attack graphs to perform static and dynamic analysis. Previous approaches have focused on the formalization of attack graphs into a Bayesian model rather than proposing mechanisms for their analysis. In this paper we propose to use efficient algorithms to make exact inference in Bayesian attack graphs, enabling the static and dynamic network risk assessments. To support the validity of our approach we have performed an extensive experimental evaluation on synthetic Bayesian attack graphs with different topologies, showing the computational advantages in terms of time and memory use of the proposed techniques when compared to existing approaches.

Decision making with partial feedback, motivated by applications including personalized medicine [22] and content recommendation [17], is receiving increasing attention from the machine learning community. These problems are formally modeled as learning from bandit feedback, where a learner repeatedly takes an action and observes a reward for the action, with the goal of maximizing reward. While bandit learning captures many problems of interest, several applications have additional structure: the action is combinatorial in nature and more detailed feedback is provided. For example, in internet applications, we often recommend sets of items and record information about the user's interaction with each individual item (e.g., click). This additional feedback is unhelpful unless it relates to the overall reward (e.g., number of clicks), and, as in previous work, we assume a linear relationship. This interaction is known as the semibandit feedback model. Typical bandit and semibandit algorithms achieve reward that is competitive with the single best fixed action, i.e., the best medical treatment or the most popular news article for everyone. This is often inadequate for recommendation applications: while the most popular articles may get some clicks, personalizing content to the users is much more effective.