There are many approaches to nonlinear SEM (structural equation modeling) but it seems that a rather straightforward approach using Isserlis' theorem has not yet been investigated although it allows the direct extension of the standard linear approach to nonlinear linear SEM. The reason may be that this method requires some symbolic calculations done at runtime. This paper describes the class of appropriate models and outlines the algorithm that calculates the covariance matrix and higher moments. Simulation studies show that the method works very well and especially that tricky models can be estimated accurately by taking higher movements into account, too.
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Bidirectional reflectance distribution functions (BRDFs) are pervasively used in computer graphics to produce realistic physically-based appearance. In recent years, several works explored using neural networks to represent BRDFs, taking advantage of neural networks' high compression rate and their ability to fit highly complex functions. However, once represented, the BRDFs will be fixed and therefore lack flexibility to take part in follow-up operations. In this paper, we present a form of "Neural BRDF algebra", and focus on both representation and operations of BRDFs at the same time. We propose a representation neural network to compress BRDFs into latent vectors, which is able to represent BRDFs accurately. We further propose several operations that can be applied solely in the latent space, such as layering and interpolation. Spatial variation is straightforward to achieve by using textures of latent vectors. Furthermore, our representation can be efficiently evaluated and sampled, providing a competitive solution to more expensive Monte Carlo layering approaches.
In this paper, we consider the problem of allocating human operators in a system with multiple semi-autonomous robots. Each robot is required to perform an independent sequence of tasks, subjected to a chance of failing and getting stuck in a fault state at every task. If and when required, a human operator can assist or teleoperate a robot. Conventional MDP techniques used to solve such problems face scalability issues due to exponential growth of state and action spaces with the number of robots and operators. In this paper we derive conditions under which the operator allocation problem is indexable, enabling the use of the Whittle index heuristic. The conditions can be easily checked to verify indexability, and we show that they hold for a wide range of problems of interest. Our key insight is to leverage the structure of the value function of individual robots, resulting in conditions that can be verified separately for each state of each robot. We apply these conditions to two types of transitions commonly seen in remote robot supervision systems. Through numerical simulations, we demonstrate the efficacy of Whittle index policy as a near-optimal and scalable approach that outperforms existing scalable methods.
Robotic skills can be learned via imitation learning (IL) using user-provided demonstrations, or via reinforcement learning (RL) using large amountsof autonomously collected experience.Both methods have complementarystrengths and weaknesses: RL can reach a high level of performance, but requiresexploration, which can be very time consuming and unsafe; IL does not requireexploration, but only learns skills that are as good as the provided demonstrations.Can a single method combine the strengths of both approaches? A number ofprior methods have aimed to address this question, proposing a variety of tech-niques that integrate elements of IL and RL. However, scaling up such methodsto complex robotic skills that integrate diverse offline data and generalize mean-ingfully to real-world scenarios still presents a major challenge. In this paper, ouraim is to test the scalability of prior IL + RL algorithms and devise a system basedon detailed empirical experimentation that combines existing components in themost effective and scalable way. To that end, we present a series of experimentsaimed at understanding the implications of each design decision, so as to develop acombined approach that can utilize demonstrations and heterogeneous prior datato attain the best performance on a range of real-world and realistic simulatedrobotic problems. Our complete method, which we call AW-Opt, combines ele-ments of advantage-weighted regression [1, 2] and QT-Opt [3], providing a unifiedapproach for integrating demonstrations and offline data for robotic manipulation.Please see //awopt.github.io for more details.
Optimal control of general nonlinear systems is a central challenge in automation. Data-driven approaches to control, enabled by powerful function approximators, have recently had great success in tackling challenging robotic applications. However, such methods often obscure the structure of dynamics and control behind black-box over-parameterized representations, thus limiting our ability to understand the closed-loop behavior. This paper adopts a hybrid-system view of nonlinear modeling and control that lends an explicit hierarchical structure to the problem and breaks down complex dynamics into simpler localized units. Therefore, we consider a sequence modeling paradigm that captures the temporal structure of the data and derive an expecation-maximization (EM) algorithm that automatically decomposes nonlinear dynamics into stochastic piecewise affine dynamical systems with nonlinear boundaries. Furthermore, we show that these time-series models naturally admit a closed-loop extension that we use to extract locally linear or polynomial feedback controllers from nonlinear experts via imitation learning. Finally, we introduce a novel hybrid realtive entropy policy search (Hb-REPS) technique that incorporates the hierarchical nature of hybrid systems and optimizes a set of time-invariant local feedback controllers derived from a locally polynomial approximation of a global value function.
We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.
We study the problem of efficient semantic segmentation for large-scale 3D point clouds. By relying on expensive sampling techniques or computationally heavy pre/post-processing steps, most existing approaches are only able to be trained and operate over small-scale point clouds. In this paper, we introduce RandLA-Net, an efficient and lightweight neural architecture to directly infer per-point semantics for large-scale point clouds. The key to our approach is to use random point sampling instead of more complex point selection approaches. Although remarkably computation and memory efficient, random sampling can discard key features by chance. To overcome this, we introduce a novel local feature aggregation module to progressively increase the receptive field for each 3D point, thereby effectively preserving geometric details. Extensive experiments show that our RandLA-Net can process 1 million points in a single pass with up to 200X faster than existing approaches. Moreover, our RandLA-Net clearly surpasses state-of-the-art approaches for semantic segmentation on two large-scale benchmarks Semantic3D and SemanticKITTI.
Matter evolved under influence of gravity from minuscule density fluctuations. Non-perturbative structure formed hierarchically over all scales, and developed non-Gaussian features in the Universe, known as the Cosmic Web. To fully understand the structure formation of the Universe is one of the holy grails of modern astrophysics. Astrophysicists survey large volumes of the Universe and employ a large ensemble of computer simulations to compare with the observed data in order to extract the full information of our own Universe. However, to evolve trillions of galaxies over billions of years even with the simplest physics is a daunting task. We build a deep neural network, the Deep Density Displacement Model (hereafter D$^3$M), to predict the non-linear structure formation of the Universe from simple linear perturbation theory. Our extensive analysis, demonstrates that D$^3$M outperforms the second order perturbation theory (hereafter 2LPT), the commonly used fast approximate simulation method, in point-wise comparison, 2-point correlation, and 3-point correlation. We also show that D$^3$M is able to accurately extrapolate far beyond its training data, and predict structure formation for significantly different cosmological parameters. Our study proves, for the first time, that deep learning is a practical and accurate alternative to approximate simulations of the gravitational structure formation of the Universe.
Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great successes. Unfortunately, the understanding on how it works remains unclear. It has the central importance to lay down the theoretic foundation for deep learning. In this work, we give a geometric view to understand deep learning: we show that the fundamental principle attributing to the success is the manifold structure in data, namely natural high dimensional data concentrates close to a low-dimensional manifold, deep learning learns the manifold and the probability distribution on it. We further introduce the concepts of rectified linear complexity for deep neural network measuring its learning capability, rectified linear complexity of an embedding manifold describing the difficulty to be learned. Then we show for any deep neural network with fixed architecture, there exists a manifold that cannot be learned by the network. Finally, we propose to apply optimal mass transportation theory to control the probability distribution in the latent space.
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-specified rank. The algorithms are simple, accurate, numerically stable, and provably correct. Moreover, each method is accompanied by an informative error bound that allows users to select parameters a priori to achieve a given approximation quality. These claims are supported by numerical experiments with real and synthetic data.
Scene text detection has been made great progress in recent years. The detection manners are evolving from axis-aligned rectangle to rotated rectangle and further to quadrangle. However, current datasets contain very little curve text, which can be widely observed in scene images such as signboard, product name and so on. To raise the concerns of reading curve text in the wild, in this paper, we construct a curve text dataset named CTW1500, which includes over 10k text annotations in 1,500 images (1000 for training and 500 for testing). Based on this dataset, we pioneering propose a polygon based curve text detector (CTD) which can directly detect curve text without empirical combination. Moreover, by seamlessly integrating the recurrent transverse and longitudinal offset connection (TLOC), the proposed method can be end-to-end trainable to learn the inherent connection among the position offsets. This allows the CTD to explore context information instead of predicting points independently, resulting in more smooth and accurate detection. We also propose two simple but effective post-processing methods named non-polygon suppress (NPS) and polygonal non-maximum suppression (PNMS) to further improve the detection accuracy. Furthermore, the proposed approach in this paper is designed in an universal manner, which can also be trained with rectangular or quadrilateral bounding boxes without extra efforts. Experimental results on CTW-1500 demonstrate our method with only a light backbone can outperform state-of-the-art methods with a large margin. By evaluating only in the curve or non-curve subset, the CTD + TLOC can still achieve the best results. Code is available at //github.com/Yuliang-Liu/Curve-Text-Detector.
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