We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the extreme learning machine (ELM) approach from low to high dimensions. With the first method the unknown solution field in $d$ dimensions is represented by a randomized feed-forward neural network, in which the hidden-layer parameters are randomly assigned and fixed while the output-layer parameters are trained. The PDE and the boundary/initial conditions, as well as the continuity conditions (for the local variant of the method), are enforced on a set of random interior/boundary collocation points. The resultant linear or nonlinear algebraic system, through its least squares solution, provides the trained values for the network parameters. With the second method the high-dimensional PDE problem is reformulated through a constrained expression based on an Approximate variant of the Theory of Functional Connections (A-TFC), which avoids the exponential growth in the number of terms of TFC as the dimension increases. The free field function in the A-TFC constrained expression is represented by a randomized neural network and is trained by a procedure analogous to the first method. We present ample numerical simulations for a number of high-dimensional linear/nonlinear stationary/dynamic PDEs to demonstrate their performance. These methods can produce accurate solutions to high-dimensional PDEs, in particular with their errors reaching levels not far from the machine accuracy for relatively lower dimensions. Compared with the physics-informed neural network (PINN) method, the current method is both cost-effective and more accurate for high-dimensional PDEs.
Carefully curated and annotated datasets are the foundation of machine learning, with particularly data-hungry deep neural networks forming the core of what is often called Artificial Intelligence (AI). Due to the massive success of deep learning applied to Earth Observation (EO) problems, the focus of the community has been largely on the development of ever-more sophisticated deep neural network architectures and training strategies largely ignoring the overall importance of datasets. For that purpose, numerous task-specific datasets have been created that were largely ignored by previously published review articles on AI for Earth observation. With this article, we want to change the perspective and put machine learning datasets dedicated to Earth observation data and applications into the spotlight. Based on a review of the historical developments, currently available resources are described and a perspective for future developments is formed. We hope to contribute to an understanding that the nature of our data is what distinguishes the Earth observation community from many other communities that apply deep learning techniques to image data, and that a detailed understanding of EO data peculiarities is among the core competencies of our discipline.
Typically, a randomized experiment is designed to test a hypothesis about the average treatment effect and sometimes hypotheses about treatment effect variation. The results of such a study may then be used to inform policy and practice for units not in the study. In this paper, we argue that given this use, randomized experiments should instead be designed to predict unit-specific treatment effects in a well-defined population. We then consider how different sampling processes and models affect the bias, variance, and mean squared prediction error of these predictions. The results indicate, for example, that problems of generalizability (differences between samples and populations) can greatly affect bias both in predictive models and in measures of error in these models. We also examine when the average treatment effect estimate outperforms unit-specific treatment effect predictive models and implications of this for planning studies.
The constant growth of DNNs makes them challenging to implement and run efficiently on traditional compute-centric architectures. Some accelerators have attempted to add more compute units and on-chip buffers to solve the memory wall problem without much success, and sometimes even worsening the issue since more compute units also require higher memory bandwidth. Prior works have proposed the design of memory-centric architectures based on the Near-Data Processing (NDP) paradigm. NDP seeks to break the memory wall by moving the computations closer to the memory hierarchy, reducing the data movements and their cost as much as possible. The 3D-stacked memory is especially appealing for DNN accelerators due to its high-density/low-energy storage and near-memory computation capabilities to perform the DNN operations massively in parallel. However, memory accesses remain as the main bottleneck for running modern DNNs efficiently. To improve the efficiency of DNN inference we present QeiHaN, a hardware accelerator that implements a 3D-stacked memory-centric weight storage scheme to take advantage of a logarithmic quantization of activations. In particular, since activations of FC and CONV layers of modern DNNs are commonly represented as powers of two with negative exponents, QeiHaN performs an implicit in-memory bit-shifting of the DNN weights to reduce memory activity. Only the meaningful bits of the weights required for the bit-shift operation are accessed. Overall, QeiHaN reduces memory accesses by 25\% compared to a standard memory organization. We evaluate QeiHaN on a popular set of DNNs. On average, QeiHaN provides $4.3x$ speedup and $3.5x$ energy savings over a Neurocube-like accelerator.
We propose a new algorithm for efficiently solving the damped Fisher matrix in large-scale scenarios where the number of parameters significantly exceeds the number of available samples. This problem is fundamental for natural gradient descent and stochastic reconfiguration. Our algorithm is based on Cholesky decomposition and is generally applicable. Benchmark results show that the algorithm is significantly faster than existing methods.
We study a novel ensemble approach for feature selection based on hierarchical stacking in cases of non-stationarity and limited number of samples with large number of features. Our approach exploits the co-dependency between features using a hierarchical structure. Initially, a machine learning model is trained using a subset of features, and then the model's output is updated using another algorithm with the remaining features to minimize the target loss. This hierarchical structure allows for flexible depth and feature selection. By exploiting feature co-dependency hierarchically, our proposed approach overcomes the limitations of traditional feature selection methods and feature importance scores. The effectiveness of the approach is demonstrated on synthetic and real-life datasets, indicating improved performance with scalability and stability compared to the traditional methods and state-of-the-art approaches.
Obtaining the solutions of partial differential equations based on various machine learning methods has drawn more and more attention in the fields of scientific computation and engineering applications. In this work, we first propose a coupled Extreme Learning Machine (called CELM) method incorporated with the physical laws to solve a class of fourth-order biharmonic equations by reformulating it into two well-posed Poisson problems. In addition, some activation functions including tangent, gauss, sine, and trigonometric (sin+cos) functions are introduced to assess our CELM method. Notably, the sine and trigonometric functions demonstrate a remarkable ability to effectively minimize the approximation error of the CELM model. In the end, several numerical experiments are performed to study the initializing approaches for both the weights and biases of the hidden units in our CELM model and explore the required number of hidden units. Numerical results show the proposed CELM algorithm is high-precision and efficient to address the biharmonic equation in both regular and irregular domains.
Many recent successful off-policy multi-agent reinforcement learning (MARL) algorithms for cooperative partially observable environments focus on finding factorized value functions, leading to convoluted network structures. Building on the structure of independent Q-learners, our LAN algorithm takes a radically different approach, leveraging a dueling architecture to learn for each agent a decentralized best-response policies via individual advantage functions. The learning is stabilized by a centralized critic whose primary objective is to reduce the moving target problem of the individual advantages. The critic, whose network's size is independent of the number of agents, is cast aside after learning. Evaluation on the StarCraft II multi-agent challenge benchmark shows that LAN reaches state-of-the-art performance and is highly scalable with respect to the number of agents, opening up a promising alternative direction for MARL research.
A fundamental problem of causal discovery is cause-effect inference, learning the correct causal direction between two random variables. Significant progress has been made through modelling the effect as a function of its cause and a noise term, which allows us to leverage assumptions about the generating function class. The recently introduced heteroscedastic location-scale noise functional models (LSNMs) combine expressive power with identifiability guarantees. LSNM model selection based on maximizing likelihood achieves state-of-the-art accuracy, when the noise distributions are correctly specified. However, through an extensive empirical evaluation, we demonstrate that the accuracy deteriorates sharply when the form of the noise distribution is misspecified by the user. Our analysis shows that the failure occurs mainly when the conditional variance in the anti-causal direction is smaller than that in the causal direction. As an alternative, we find that causal model selection through residual independence testing is much more robust to noise misspecification and misleading conditional variance.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
We introduce a generic framework that reduces the computational cost of object detection while retaining accuracy for scenarios where objects with varied sizes appear in high resolution images. Detection progresses in a coarse-to-fine manner, first on a down-sampled version of the image and then on a sequence of higher resolution regions identified as likely to improve the detection accuracy. Built upon reinforcement learning, our approach consists of a model (R-net) that uses coarse detection results to predict the potential accuracy gain for analyzing a region at a higher resolution and another model (Q-net) that sequentially selects regions to zoom in. Experiments on the Caltech Pedestrians dataset show that our approach reduces the number of processed pixels by over 50% without a drop in detection accuracy. The merits of our approach become more significant on a high resolution test set collected from YFCC100M dataset, where our approach maintains high detection performance while reducing the number of processed pixels by about 70% and the detection time by over 50%.