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Learning the graphical structure of Bayesian networks is key to describing data-generating mechanisms in many complex applications but poses considerable computational challenges. Observational data can only identify the equivalence class of the directed acyclic graph underlying a Bayesian network model, and a variety of methods exist to tackle the problem. Under certain assumptions, the popular PC algorithm can consistently recover the correct equivalence class by reverse-engineering the conditional independence (CI) relationships holding in the variable distribution. The dual PC algorithm is a novel scheme to carry out the CI tests within the PC algorithm by leveraging the inverse relationship between covariance and precision matrices. By exploiting block matrix inversions we can also perform tests on partial correlations of complementary (or dual) conditioning sets. The multiple CI tests of the dual PC algorithm proceed by first considering marginal and full-order CI relationships and progressively moving to central-order ones. Simulation studies show that the dual PC algorithm outperforms the classic PC algorithm both in terms of run time and in recovering the underlying network structure, even in the presence of deviations from Gaussianity. Additionally, we show that the dual PC algorithm applies for Gaussian copula models, and demonstrate its performance in that setting.

We establish globally optimal solutions to a class of fractional optimization problems on a class of constraint sets, whose key characteristics are as follows: 1) The numerator and the denominator of the objective function are both convex, semi-algebraic, Lipschitz continuous and differentiable with Lipschitz continuous gradients on the constraint set. 2) The constraint set is closed, convex and semi-algebraic. Compared with Dinkelbach's approach, our novelty falls into the following aspects: 1) Dinkelbach's has to solve a concave maximization problem in each iteration, which is nontrivial to obtain a solution, while ours only needs to conduct one proximity gradient operation in each iteration. 2) Dinkelbach's requires at least one nonnegative point for the numerator to proceed the algorithm, but ours does not, which is available to a much wider class of situations. 3) Dinkelbach's requires a closed and bounded constraint set, while ours only needs the closedness but not necessarily the boundedness. Therefore, our approach is viable for many more practical models, like optimizing the Sharpe ratio (SR) or the Information ratio in mathematical finance. Numerical experiments show that our approach achieves the ground-truth solutions in two simple examples. For real-world financial data, it outperforms several existing approaches for SR maximization.

Integer linear programming (ILP) models a wide range of practical combinatorial optimization problems and has significant impacts in industry and management sectors. This work proposes new characterizations of ILP with the concept of boundary solutions. Motivated by the new characterizations, we develop an efficient local search solver, which is the first local search solver for general ILP validated on a large heterogeneous problem dataset. We propose a new local search framework that switches between three modes, namely Search, Improve, and Restore modes. We design tailored operators adapted to different modes, thus improving the quality of the current solution according to different situations. For the Search and Restore modes, we propose an operator named tight move, which adaptively modifies variables' values, trying to make some constraint tight. For the Improve mode, an efficient operator lift move is proposed to improve the quality of the objective function while maintaining feasibility. Putting these together, we develop a local search solver for integer linear programming called Local-ILP. Experiments conducted on the MIPLIB dataset show the effectiveness of our solver in solving large-scale hard integer linear programming problems within a reasonably short time. Local-ILP is competitive and complementary to the state-of-the-art commercial solver Gurobi and significantly outperforms the state-of-the-art non-commercial solver SCIP. Moreover, our solver establishes new records for 6 MIPLIB open instances. The theoretical analysis of our algorithm is also presented, which shows our algorithm could avoid visiting unnecessary regions and also maintain good connectivity of targeted solutions.

We explore sim-to-real transfer of deep reinforcement learning controllers for a heavy vehicle with active suspensions designed for traversing rough terrain. While related research primarily focuses on lightweight robots with electric motors and fast actuation, this study uses a forestry vehicle with a complex hydraulic driveline and slow actuation. We simulate the vehicle using multibody dynamics and apply system identification to find an appropriate set of simulation parameters. We then train policies in simulation using various techniques to mitigate the sim-to-real gap, including domain randomization, action delays, and a reward penalty to encourage smooth control. In reality, the policies trained with action delays and a penalty for erratic actions perform at nearly the same level as in simulation. In experiments on level ground, the motion trajectories closely overlap when turning to either side, as well as in a route tracking scenario. When faced with a ramp that requires active use of the suspensions, the simulated and real motions are in close alignment. This shows that the actuator model together with system identification yields a sufficiently accurate model of the actuators. We observe that policies trained without the additional action penalty exhibit fast switching or bang-bang control. These present smooth motions and high performance in simulation but transfer poorly to reality. We find that policies make marginal use of the local height map for perception, showing no indications of look-ahead planning. However, the strong transfer capabilities entail that further development concerning perception and performance can be largely confined to simulation.

We study a wireless jamming problem consisting of the competition between a legitimate receiver and a jammer, as a zero-sum game with the value to maximize/minimize being the channel capacity at the receiver's side. Most of the approaches found in the literature consider the two players to be stationary nodes. Instead, we investigate what happens when they can change location, specifically moving along a linear geometry. We frame this at first as a static game, which can be solved in closed form, and subsequently we extend it to a dynamic game, under three different versions for what concerns completeness/perfection of mutual information about the adversary's position, corresponding to different assumptions of concealment/sequentiality of the moves, respectively. We first provide some theoretical conditions that hold for the static game and also help identify good strategies valid under any setup, including dynamic games. Since dynamic games, although more realistic, are characterized by an exploding strategy space, we exploit reinforcement learning to obtain efficient strategies leading to equilibrium outcomes. We show how theoretical findings can be used to train smart agents to play the game, and validate our approach in practical setups.

Discourse analysis is an important task because it models intrinsic semantic structures between sentences in a document. Discourse markers are natural representations of discourse in our daily language. One challenge is that the markers as well as pre-defined and human-labeled discourse relations can be ambiguous when describing the semantics between sentences. We believe that a better approach is to use a contextual-dependent distribution over the markers to express discourse information. In this work, we propose to learn a Distributed Marker Representation (DMR) by utilizing the (potentially) unlimited discourse marker data with a latent discourse sense, thereby bridging markers with sentence pairs. Such representations can be learned automatically from data without supervision, and in turn provide insights into the data itself. Experiments show the SOTA performance of our DMR on the implicit discourse relation recognition task and strong interpretability. Our method also offers a valuable tool to understand complex ambiguity and entanglement among discourse markers and manually defined discourse relations.

In Wireless Networked Control Systems (WNCSs), the feedback control loops are closed over a wireless communication network. The proliferation of WNCSs requires efficient network resource management mechanisms since the control performance is significantly affected by the impairments caused by network limitations. In conventional communication networks, the amount of transmitted data is one of the key performance indicators. In contrast, in WNCSs, the efficiency of the network is measured by its ability to facilitate control applications, and the data transmission rate should be limited to avoid network congestion. In this work, we consider an experimental setup where multiple control loops share a wireless communication network. Our testbed comprises up to five control loops that include Zolertia Re-Mote devices implementing IEEE 802.15.4 standard. We propose a novel relevance- and network-aware transport layer (TL) scheme for WNCSs. The proposed scheme admits the most important measurements for the control process into the network while taking current network conditions into account. Moreover, we propose a mechanism for the scheme parameters adaptation in dynamic scenarios with unknown network statistics. Unlike the conventional TL mechanisms failing to provide adequate control performance due to either congestion in the network or inefficient utilization of available resources, our method prevents network congestion while keeping the control performance high. We argue that relevance- and network-awareness are critical components of network protocol design to avoid control performance degradation in practice.

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either low-dimensional projections of neural activity, or on learning dynamical systems that explicitly relate to the neural state over time. We discuss how these two approaches are interrelated by considering dynamical systems as representative of flows on a low-dimensional manifold. Building on this concept, we propose a new decomposed dynamical system model that represents complex non-stationary and nonlinear dynamics of time series data as a sparse combination of simpler, more interpretable components. Our model is trained through a dictionary learning procedure, where we leverage recent results in tracking sparse vectors over time. The decomposed nature of the dynamics is more expressive than previous switched approaches for a given number of parameters and enables modeling of overlapping and non-stationary dynamics. In both continuous-time and discrete-time instructional examples we demonstrate that our model can well approximate the original system, learn efficient representations, and capture smooth transitions between dynamical modes, focusing on intuitive low-dimensional non-stationary linear and nonlinear systems. Furthermore, we highlight our model's ability to efficiently capture and demix population dynamics generated from multiple independent subnetworks, a task that is computationally impractical for switched models. Finally, we apply our model to neural "full brain" recordings of C. elegans data, illustrating a diversity of dynamics that is obscured when classified into discrete states.

Detection of the outliers is pivotal for any machine learning model deployed and operated in real-world. It is essential for the Deep Neural Networks that were shown to be overconfident with such inputs. Moreover, even deep generative models that allow estimation of the probability density of the input fail in achieving this task. In this work, we concentrate on the specific type of these models: Variational Autoencoders (VAEs). First, we unveil a significant theoretical flaw in the assumption of the classical VAE model. Second, we enforce an accommodating topological property to the image of the deep neural mapping to the latent space: compactness to alleviate the flaw and obtain the means to provably bound the image within the determined limits by squeezing both inliers and outliers together. We enforce compactness using two approaches: (i) Alexandroff extension and (ii) fixed Lipschitz continuity constant on the mapping of the encoder of the VAEs. Finally and most importantly, we discover that the anomalous inputs predominantly tend to land on the vacant latent holes within the compact space, enabling their successful identification. For that reason, we introduce a specifically devised score for hole detection and evaluate the solution against several baseline benchmarks achieving promising results.

In order to overcome the expressive limitations of graph neural networks (GNNs), we propose the first method that exploits vector flows over graphs to develop globally consistent directional and asymmetric aggregation functions. We show that our directional graph networks (DGNs) generalize convolutional neural networks (CNNs) when applied on a grid. Whereas recent theoretical works focus on understanding local neighbourhoods, local structures and local isomorphism with no global information flow, our novel theoretical framework allows directional convolutional kernels in any graph. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then we propose the use of the Laplacian eigenvectors as such vector field, and we show that the method generalizes CNNs on an n-dimensional grid, and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. Finally, we bring the power of CNN data augmentation to graphs by providing a means of doing reflection, rotation and distortion on the underlying directional field. We evaluate our method on different standard benchmarks and see a relative error reduction of 8\% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset. An important outcome of this work is that it enables to translate any physical or biological problems with intrinsic directional axes into a graph network formalism with an embedded directional field.