We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of $1$-bit quantization -- allow a high accuracy approximation of the underlying kernels, and the approximation error decays at least polynomially fast as the dimension of the RFFs increases. We also show that the quantized RFFs can be further compressed, yielding an excellent trade-off between memory use and accuracy. Namely, the approximation error now decays exponentially as a function of the bits used. Moreover, we empirically show by testing the performance of our methods on several machine learning tasks that our method compares favorably to other state of the art quantization methods in this context.

In this work we study the orbit recovery problem, which is a natural abstraction for the problem of recovering a planted signal from noisy measurements under unknown group actions. Many important inverse problems in statistics, engineering and the sciences fit into this framework. Prior work has studied cases when the group is discrete and/or abelian. However fundamentally new techniques are needed in order to handle more complex group actions. Our main result is a quasi-polynomial time algorithm to solve orbit recovery over $SO(3)$ - i.e. the cryo-electron tomography problem which asks to recover the three-dimensional structure of a molecule from noisy measurements of randomly rotated copies of it. We analyze a variant of the frequency marching heuristic in the framework of smoothed analysis. Our approach exploits the layered structure of the invariant polynomials, and simultaneously yields a new class of tensor decomposition algorithms that work in settings when the tensor is not low-rank but rather where the factors are algebraically related to each other by a group action.

Machine learning has enabled the prediction of quantum chemical properties with high accuracy and efficiency, allowing to bypass computationally costly ab initio calculations. Instead of training on a fixed set of properties, more recent approaches attempt to learn the electronic wavefunction (or density) as a central quantity of atomistic systems, from which all other observables can be derived. This is complicated by the fact that wavefunctions transform non-trivially under molecular rotations, which makes them a challenging prediction target. To solve this issue, we introduce general SE(3)-equivariant operations and building blocks for constructing deep learning architectures for geometric point cloud data and apply them to reconstruct wavefunctions of atomistic systems with unprecedented accuracy. Our model reduces prediction errors by up to two orders of magnitude compared to the previous state-of-the-art and makes it possible to derive properties such as energies and forces directly from the wavefunction in an end-to-end manner. We demonstrate the potential of our approach in a transfer learning application, where a model trained on low accuracy reference wavefunctions implicitly learns to correct for electronic many-body interactions from observables computed at a higher level of theory. Such machine-learned wavefunction surrogates pave the way towards novel semi-empirical methods, offering resolution at an electronic level while drastically decreasing computational cost. While we focus on physics applications in this contribution, the proposed equivariant framework for deep learning on point clouds is promising also beyond, say, in computer vision or graphics.

Artificial Intelligence has many benefits, but one of the biggest benefits of it is faster technological advancements. Artificial intelligence is now widely used in research, which means it will quickly learn how to find results for many questions that the world is exploring. This means that researchers will be free to devise new parameters and objectives. Artificial Intelligence keeps developing, and that raises the question: will AI or robotics one day replace us in the workplace? Or will AI replace developers?

As artificial intelligence (AI) systems get increasingly complex, they are being used to make forecasts – or rather generate predictive model results – in more and more areas of our lives. But at the same time, concerns are on the rise about reliability, amid widening margins of error in elaborate AI predictions. How can we address these concerns? Management science offers a set of tools that can make AI systems more trustworthy, according to Thomas G Dietterich, professor emeritus and director of intelligent systems research at Oregon State University. During a webinar on the AI for Good platform hosted by the International Telecommunication Union (ITU), Dietterich told the audience that the discipline that brings human decision-makers to the top of their game can also be applied to machines.

The demand of probabilistic time series forecasting has been recently raised in various dynamic system scenarios, for example, system identification and prognostic and health management of machines. To this end, we combine the advances in both deep generative models and state space model (SSM) to come up with a novel, data-driven deep probabilistic sequence model. Specially, we follow the popular encoder-decoder generative structure to build the recurrent neural networks (RNN) assisted variational sequence model on an augmented recurrent input space, which could induce rich stochastic sequence dependency. Besides, in order to alleviate the issue of inconsistency between training and predicting as well as improving the mining of dynamic patterns, we (i) propose using a hybrid output as input at next time step, which brings training and predicting into alignment; and (ii) further devise a generalized auto-regressive strategy that encodes all the historical dependencies at current time step. Thereafter, we first investigate the methodological characteristics of the proposed deep probabilistic sequence model on toy cases, and then comprehensively demonstrate the superiority of our model against existing deep probabilistic SSM models through extensive numerical experiments on eight system identification benchmarks from various dynamic systems. Finally, we apply our sequence model to a real-world centrifugal compressor sensor data forecasting problem, and again verify its outstanding performance by quantifying the time series predictive distribution.

In this paper, we propose a gradient boosting algorithm for large-scale regression problems called \textit{Gradient Boosted Binary Histogram Ensemble} (GBBHE) based on binary histogram partition and ensemble learning. From the theoretical perspective, by assuming the H\"{o}lder continuity of the target function, we establish the statistical convergence rate of GBBHE in the space $C^{0,\alpha}$ and $C^{1,0}$, where a lower bound of the convergence rate for the base learner demonstrates the advantage of boosting. Moreover, in the space $C^{1,0}$, we prove that the number of iterations to achieve the fast convergence rate can be reduced by using ensemble regressor as the base learner, which improves the computational efficiency. In the experiments, compared with other state-of-the-art algorithms such as gradient boosted regression tree (GBRT), Breiman's forest, and kernel-based methods, our GBBHE algorithm shows promising performance with less running time on large-scale datasets.

This is an end-to-end Project of performing Extract-Transform-Load and Exploratory Data Analysis on a real-world dataset, and then applying several different machine learning algorithms to solve a supervised regression problem on the dataset. Our goal is to accurately predict power output given a set of environmental readings from various sensors in a natural gas-fired power generation plant. Power generation is a complex process, and understanding and predicting power output is an important element in managing a plant and its connection to the power grid. The operators of a regional power grid create predictions of power demand based on historical information and environmental factors (e.g., temperature). They then compare the predictions against available resources (e.g., coal, natural gas, nuclear, solar, wind, hydro power plants).

The names of many of the new companies and technologies created to combat the effects of climate change on marine ecosystems can evoke thrilling acts of derring-do on the high seas. WaveKiller uses compressed air systems to create "walls" of bubbles up to 50 feet thick, to guard against erosion and contain waste and oil spills. The Inceptor is a solar-powered barge deployed by the Dutch nongovernmental organization Ocean Cleanup along rivers in Southeast Asia to gather tons of waste before it hits the sea. Saildrone and WasteShark build and deploy fleets of autonomous drones to ply the oceans, gathering meteorological and marine data in the former case and trash in the latter. This sample of (often menacingly-named) technologies represents the increasingly diverse approaches to combat marine degradation--diversity which is desperately needed, as climate change wages war on the health of the world's oceans on many different fronts.

We propose an end-to-end deep learning framework that comprehensively solves the inverse wave scattering problem across all length scales. Our framework consists of the newly introduced wide-band butterfly network coupled with a simple training procedure that dynamically injects noise during training. While our trained network provides competitive results in classical imaging regimes, most notably it also succeeds in the super-resolution regime where other comparable methods fail. This encompasses both (i) reconstruction of scatterers with sub-wavelength geometric features, and (ii) accurate imaging when two or more scatterers are separated by less than the classical diffraction limit. We demonstrate these properties are retained even in the presence of strong noise and extend to scatterers not previously seen in the training set. In addition, our network is straightforward to train requiring no restarts and has an online runtime that is an order of magnitude faster than optimization-based algorithms. We perform experiments with a variety of wave scattering mediums and we demonstrate that our proposed framework outperforms both classical inversion and competing network architectures that specialize in oscillatory wave scattering data.