An Open Problem on Sparse Representations in Unions of Bases

We consider sparse representations of signals from redundant dictionaries which are unions of several orthonormal bases. The spark introduced by Donoho and Elad plays an important role in sparse representations. However, numerical computations of sparks are generally combinatorial. For unions of several orthonormal bases, two lower bounds on the spark via the mutual coherence were established in previous work. We constructively prove that both of them are tight. Our main results give positive answers to Gribonval and Nielsens open problem on sparse representations in unions of orthonormal bases. Constructive proofs rely on a family of mutually unbiased bases which first appears in quantum information theory.

CARlasso: An R package for the estimation of sparse microbial networks with predictors

Microbiome data analyses require statistical tools that can simultaneously decode microbes reactions to the environment and interactions among microbes. We introduce CARlasso, the first user-friendly open-source and publicly available R package to fit a chain graph model for the inference of sparse microbial networks that represent both interactions among nodes and effects of a set of predictors. Unlike in standard regression approaches, the edges represent the correct conditional structure among responses and predictors that allows the incorporation of prior knowledge from controlled experiments. In addition, CARlasso 1) enforces sparsity in the network via LASSO; 2) allows for an adaptive extension to include different shrinkage to different edges; 3) is computationally inexpensive through an efficient Gibbs sampling algorithm so it can equally handle small and big data; 4) allows for continuous, binary, counting and compositional responses via proper hierarchical structure, and 5) has a similar syntax to lm for ease of use. The package also supports Bayesian graphical LASSO and several of its hierarchical models as well as lower level one-step sampling functions of the CAR-LASSO model for users to extend.

An aggregated model for Karlin stable processes

An aggregated model is proposed, of which the partial-sum process scales to the Karlin stable processes recently investigated in the literature. The limit extremes of the proposed model, when having regularly-varying tails, are characterized by the convergence of the corresponding point processes. The proposed model is an extension of an aggregated model proposed by Enriquez (2004) in order to approximate fractional Brownian motions with Hurst index $Hin(0,1/2)$, and is of a different nature of the other recently investigated Karlin models which are essentially based on infinite urn schemes.

The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models

Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. We approximate the marginal posterior precision of the precision matrix via Laplace approximation under different priors: a flat prior, the conjugate prior Normal-Wishart, the unconfounded prior Normal-Matrix Generalized Inverse Gaussian (MGIG) and a general independent prior. We show that the approximated posterior precision is not a function of the design matrix for the cases of the Normal-Wishart and flat prior, but it is for the cases of the Normal-MGIG and the general independent prior. However, for the Normal-MGIG and the general independent prior, we find a sharp upper bound on the approximated posterior precision that does not involve the design matrix which translates into a bound on the information that could be extracted from a given experiment. We confirm the theoretical findings via a simulation study comparing the Steins loss difference between random versus no experiment (design matrix equal to zero). Our findings provide practical advice for domain scientists conducting experiments to decode the relationships between a multidimensional response and a set of predictors.

Learning without Knowing: Unobserved Context in Continuous Transfer Reinforcement Learning

In this paper, we consider a transfer Reinforcement Learning (RL) problem in continuous state and action spaces, under unobserved contextual information. For example, the context can represent the mental view of the world that an expert agent has formed through past interactions with this world. We assume that this context is not accessible to a learner agent who can only observe the expert data. Then, our goal is to use the context-aware expert data to learn an optimal context-unaware policy for the learner using only a few new data samples. Such problems are typically solved using imitation learning that assumes that both the expert and learner agents have access to the same information. However, if the learner does not know the expert context, using the expert data alone will result in a biased learner policy and will require many new data samples to improve. To address this challenge, in this paper, we formulate the learning problem as a causal bound-constrained Multi-Armed-Bandit (MAB) problem. The arms of this MAB correspond to a set of basis policy functions that can be initialized in an unsupervised way using the expert data and represent the different expert behaviors affected by the unobserved context. On the other hand, the MAB constraints correspond to causal bounds on the accumulated rewards of these basis policy functions that we also compute from the expert data. The solution to this MAB allows the learner agent to select the best basis policy and improve it online. And the use of causal bounds reduces the exploration variance and, therefore, improves the learning rate. We provide numerical experiments on an autonomous driving example that show that our proposed transfer RL method improves the learners policy faster compared to existing imitation learning methods and enjoys much lower variance during training.

You Never Cluster Alone

Recent advances in self-supervised learning with instance-level contrastive objectives facilitate unsupervised clustering. However, a standalone datum is not perceiving the context of the holistic cluster, and may undergo sub-optimal assignment. In this paper, we extend the mainstream contrastive learning paradigm to a cluster-level scheme, where all the data subjected to the same cluster contribute to a unified representation that encodes the context of each data group. Contrastive learning with this representation then rewards the assignment of each datum. To implement this vision, we propose twin-contrast clustering (TCC). We define a set of categorical variables as clustering assignment confidence, which links the instance-level learning track with the cluster-level one. On one hand, with the corresponding assignment variables being the weight, a weighted aggregation along the data points implements the set representation of a cluster. We further propose heuristic cluster augmentation equivalents to enable cluster-level contrastive learning. On the other hand, we derive the evidence lower-bound of the instance-level contrastive objective with the assignments. By reparametrizing the assignment variables, TCC is trained end-to-end, requiring no alternating steps. Extensive experiments show that TCC outperforms the state-of-the-art on challenging benchmarks.

STEP: Spatial-Temporal Network Security Event Prediction

Network security events prediction helps network operators to take response strategies from a proactive perspective, and reduce the cost caused by network attacks, which is of great significance for maintaining the security of the entire network. Most of the existing event prediction methods rely on temporal characteristics and are dedicated to exploring time series predictions, but ignoring the spatial relationship between hosts. This paper combines the temporal and spatial characteristics of security events and proposes a spatial-temporal event prediction model, named STEP. In particular, STEP formulates the security events prediction into a spatial-temporal sequence prediction. STEP utilizes graph convolution operation to capture the spatial characteristics of hosts in the network, and adopts the long short term memory (LSTM) to capture the dynamic temporal dependency of events. This paper verifies the proposed STEP scheme on two public data sets. The experimental results show that the prediction accuracy of security events under STEP is higher than that of benchmark models such as LSTM, ConvLSTM. Besides, STEP achieves high prediction accuracy when we predict events from different lengths of sequence.

Packet-Level Adversarial Network Traffic Crafting using Sequence Generative Adversarial Networks

The surge in the internet of things (IoT) devices seriously threatens the current IoT security landscape, which requires a robust network intrusion detection system (NIDS). Despite superior detection accuracy, existing machine learning or deep learning based NIDS are vulnerable to adversarial examples. Recently, generative adversarial networks (GANs) have become a prevailing method in adversarial examples crafting. However, the nature of discrete network traffic at the packet level makes it hard for GAN to craft adversarial traffic as GAN is efficient in generating continuous data like image synthesis. Unlike previous methods that convert discrete network traffic into a grayscale image, this paper gains inspiration from SeqGAN in sequence generation with policy gradient. Based on the structure of SeqGAN, we propose Attack-GAN to generate adversarial network traffic at packet level that complies with domain constraints. Specifically, the adversarial packet generation is formulated into a sequential decision making process. In this case, each byte in a packet is regarded as a token in a sequence. The objective of the generator is to select a token to maximize its expected end reward. To bypass the detection of NIDS, the generated network traffic and benign traffic are classified by a black-box NIDS. The prediction results returned by the NIDS are fed into the discriminator to guide the update of the generator. We generate malicious adversarial traffic based on a real public available dataset with attack functionality unchanged. The experimental results validate that the generated adversarial samples are able to deceive many existing black-box NIDS.

Bayesian Conditional Auto-Regressive LASSO Models to Learn Sparse Microbial Networks with Predictors

Microbiome data analyses require statistical models that can simultaneously decode microbes reactions to the environment and interactions among microbes. While a multiresponse linear regression model seems like a straightforward solution, we argue that treating it as a graphical model is flawed given that the regression coefficient matrix does not encode the conditional dependence structure between response and predictor nodes because it does not represent the adjacency matrix. This observation is especially important in biological settings when we have prior knowledge on the edges from specific experimental interventions that can only be properly encoded under a conditional dependence model. Here, we propose a chain graph model with two sets of nodes (predictors and responses) whose solution yields a graph with edges that indeed represent conditional dependence and thus, agrees with the experimenters intuition on the average behavior of nodes under treatment. The solution to our model is sparse via Bayesian LASSO and is also guaranteed to be the sparse solution to a Conditional Auto-Regressive (CAR) model. In addition, we propose an adaptive extension so that different shrinkage can be applied to different edges to incorporate edge-specific prior knowledge. Our model is computationally inexpensive through an efficient Gibbs sampling algorithm and can account for binary, counting, and compositional responses via appropriate hierarchical structure. We apply our model to a human gut and a soil microbial compositional datasets and we highlight that CAR-LASSO can estimate biologically meaningful network structures in the data. The CAR-LASSO software is available as an R package at https://github.com/YunyiShen/CAR-LASSO.

Deformable and robust core-shell protein microcapsules templated by liquid-liquid phase separated microdroplets

Microcapsules are a key class of microscale materials with applications in areas ranging from personal care to biomedicine, and with increasing potential to act as extracellular matrix (ECM) models of hollow organs or tissues. Such capsules are conventionally generated from non-ECM materials including synthetic polymers. Here, we fabricated robust microcapsules with controllable shell thickness from physically- and enzymatically-crosslinked gelatin and achieved a core-shell architecture by exploiting a liquid-liquid phase separated aqueous dispersed phase system in a one-step microfluidic process. Microfluidic mechanical testing revealed that the mechanical robustness of thicker-shell capsules could be controlled through modulation of the shell thickness. Furthermore, the microcapsules demonstrated environmentally-responsive deformation, including buckling by osmosis and external mechanical forces. A sequential release of cargo species was obtained through the degradation of the capsules. Stability measurements showed the capsules were stable at 37 {deg}C for more than two weeks. Finally, all-aqueous liquid-liquid phase separated and multiphase liquid-liquid phase separated systems were generated with the gel-sol transition of microgel precursors. These smart capsules are promising models of hollow biostructures, microscale drug carriers, and building blocks or compartments for active soft materials and robots.