pwc-archive/papers-with-abstracts huggingface dataset:
Beyond Smoothness: Incorporating Low-Rank Analysis into Nonparametric Density Estimation
Authors: Robert A. Vandermeulen, Antoine Ledent
Date: 2022-04-02 00:00:00
Proceeding: NeurIPS 2021 12
Tasks: Density Estimation

The construction and theoretical analysis of the most popular universally consistent nonparametric density estimators hinge on one functional property: smoothness. In this paper we investigate the theoretical implications of incorporating a multi-view latent variable model, a type of low-rank model, into nonparametric density estimation. To do this we perform extensive analysis on histogram-style estimators that integrate a multi-view model. Our analysis culminates in showing that there exists a universally consistent histogram-style estimator that converges to any multi-view model with a finite number of Lipschitz continuous components at a rate of $\widetilde{O}(1/\sqrt[3]{n})$ in $L^1$ error. In contrast, the standard histogram estimator can converge at a rate slower than $1/\sqrt[d]{n}$ on the same class of densities. We also introduce a new nonparametric latent variable model based on the Tucker decomposition. A rudimentary implementation of our estimators experimentally demonstrates a considerable performance improvement over the standard histogram estimator. We also provide a thorough analysis of the sample complexity of our Tucker decomposition-based model and a variety of other results. Thus, our paper provides solid theoretical foundations for extending low-rank techniques to the nonparametric setting
Model-Free and Model-Based Policy Evaluation when Causality is Uncertain
Authors: David Bruns-Smith
Date: 2022-04-02 00:00:00
Tasks: model, Off-policy evaluation, Sensitivity, valid

When decision-makers can directly intervene, policy evaluation algorithms give valid causal estimates. In off-policy evaluation (OPE), there may exist unobserved variables that both impact the dynamics and are used by the unknown behavior policy. These "confounders" will introduce spurious correlations and naive estimates for a new policy will be biased. We develop worst-case bounds to assess sensitivity to these unobserved confounders in finite horizons when confounders are drawn iid each period. We demonstrate that a model-based approach with robust MDPs gives sharper lower bounds by exploiting domain knowledge about the dynamics. Finally, we show that when unobserved confounders are persistent over time, OPE is far more difficult and existing techniques produce extremely conservative bounds.
Random Fully Connected Neural Networks as Perturbatively Solvable Hierarchies
Authors: Boris Hanin
Date: 2022-04-03 00:00:00

This article considers fully connected neural networks with Gaussian random weights and biases as well as $L$ hidden layers, each of width proportional to a large parameter $n$. For polynomially bounded non-linearities we give sharp estimates in powers of $1/n$ for the joint cumulants of the network output and its derivatives. Moreover, we show that network cumulants form a perturbatively solvable hierarchy in powers of $1/n$ in that $k$-th order cumulants in one layer have recursions that depend to leading order in $1/n$ only on $j$-th order cumulants at the previous layer with $j\leq k$. By solving a variety of such recursions, however, we find that the depth-to-width ratio $L/n$ plays the role of an effective network depth, controlling both the scale of fluctuations at individual neurons and the size of inter-neuron correlations. Thus, while the cumulant recursions we derive form a hierarchy in powers of $1/n$, contributions of order $1/n^k$ often grow like $L^k$ and are hence non-negligible at positive $L/n$. We use this to study a somewhat simplified version of the exploding and vanishing gradient problem, proving that this particular variant occurs if and only if $L/n$ is large. Several key ideas in this article were first developed at a physics level of rigor in a recent monograph of Daniel A. Roberts, Sho Yaida, and the author. This article not only makes these ideas mathematically precise but also significantly extends them, opening the way to obtaining corrections to all orders in $1/n$.
Adaptive Stochastic MPC under Unknown Noise Distribution
Authors: Charis Stamouli, Anastasios Tsiamis, Manfred Morari, George J. Pappas
Date: 2022-04-03 00:00:00
Tasks: valid

In this paper, we address the stochastic MPC (SMPC) problem for linear systems, subject to chance state constraints and hard input constraints, under unknown noise distribution. First, we reformulate the chance state constraints as deterministic constraints depending only on explicit noise statistics. Based on these reformulated constraints, we design a distributionally robust and robustly stable benchmark SMPC algorithm for the ideal setting of known noise statistics. Then, we employ this benchmark controller to derive a novel robustly stable adaptive SMPC scheme that learns the necessary noise statistics online, while guaranteeing time-uniform satisfaction of the unknown reformulated state constraints with high probability. The latter is achieved through the use of confidence intervals which rely on the empirical noise statistics and are valid uniformly over time. Moreover, control performance is improved over time as more noise samples are gathered and better estimates of the noise statistics are obtained, given the online adaptation of the estimated reformulated constraints. Additionally, in tracking problems with multiple successive targets our approach leads to an online-enlarged domain of attraction compared to robust tube-based MPC. A numerical simulation of a DC-DC converter is used to demonstrate the effectiveness of the developed methodology.
Fitting an immersed submanifold to data via Sussmann's orbit theorem
Authors: Joshua Hanson, Maxim Raginsky
Date: 2022-04-03 00:00:00
Tasks: Decoder

This paper describes an approach for fitting an immersed submanifold of a finite-dimensional Euclidean space to random samples. The reconstruction mapping from the ambient space to the desired submanifold is implemented as a composition of an encoder that maps each point to a tuple of (positive or negative) times and a decoder given by a composition of flows along finitely many vector fields starting from a fixed initial point. The encoder supplies the times for the flows. The encoder-decoder map is obtained by empirical risk minimization, and a high-probability bound is given on the excess risk relative to the minimum expected reconstruction error over a given class of encoder-decoder maps. The proposed approach makes fundamental use of Sussmann's orbit theorem, which guarantees that the image of the reconstruction map is indeed contained in an immersed submanifold.
Byzantine-Robust Federated Linear Bandits
Authors: Ali Jadbabaie, Haochuan Li, Jian Qian, Yi Tian
Date: 2022-04-03 00:00:00
Tasks: Federated Learning

In this paper, we study a linear bandit optimization problem in a federated setting where a large collection of distributed agents collaboratively learn a common linear bandit model. Standard federated learning algorithms applied to this setting are vulnerable to Byzantine attacks on even a small fraction of agents. We propose a novel algorithm with a robust aggregation oracle that utilizes the geometric median. We prove that our proposed algorithm is robust to Byzantine attacks on fewer than half of agents and achieves a sublinear $\tilde{\mathcal{O}}({T^{3/4}})$ regret with $\mathcal{O}(\sqrt{T})$ steps of communication in $T$ steps. Moreover, we make our algorithm differentially private via a tree-based mechanism. Finally, if the level of corruption is known to be small, we show that using the geometric median of mean oracle for robust aggregation further improves the regret bound.
Learning Linear Symmetries in Data Using Moment Matching
Authors: Colin Hagemeyer
Date: 2022-04-04 00:00:00
Tasks: Data Augmentation

It is common in machine learning and statistics to use symmetries derived from expert knowledge to simplify problems or improve performance, using methods like data augmentation or penalties. In this paper we consider the unsupervised and semi-supervised problems of learning such symmetries in a distribution directly from data in a model-free fashion. We show that in the worst case this problem is as difficult as the graph automorphism problem. However, if we restrict to the case where the covariance matrix has unique eigenvalues, then the eigenvectors will also be eigenvectors of the symmetry transformation. If we further restrict to finding orthogonal symmetries, then the eigenvalues will be either be 1 or -1, and the problem reduces to determining which eigenvectors are which. We develop and compare theoretically and empirically the effectiveness of different methods of selecting which eigenvectors should have eigenvalue -1 in the symmetry transformation, and discuss how to extend this approach to non-orthogonal cases where we have labels
Neural Estimation of the Rate-Distortion Function With Applications to Operational Source Coding
Authors: Eric Lei, Hamed Hassani, Shirin Saeedi Bidokhti
Date: 2022-04-04 00:00:00
Tasks: Data Compression

A fundamental question in designing lossy data compression schemes is how well one can do in comparison with the rate-distortion function, which describes the known theoretical limits of lossy compression. Motivated by the empirical success of deep neural network (DNN) compressors on large, real-world data, we investigate methods to estimate the rate-distortion function on such data, which would allow comparison of DNN compressors with optimality. While one could use the empirical distribution of the data and apply the Blahut-Arimoto algorithm, this approach presents several computational challenges and inaccuracies when the datasets are large and high-dimensional, such as the case of modern image datasets. Instead, we re-formulate the rate-distortion objective, and solve the resulting functional optimization problem using neural networks. We apply the resulting rate-distortion estimator, called NERD, on popular image datasets, and provide evidence that NERD can accurately estimate the rate-distortion function. Using our estimate, we show that the rate-distortion achievable by DNN compressors are within several bits of the rate-distortion function for real-world datasets. Additionally, NERD provides access to the rate-distortion achieving channel, as well as samples from its output marginal. Therefore, using recent results in reverse channel coding, we describe how NERD can be used to construct an operational one-shot lossy compression scheme with guarantees on the achievable rate and distortion. Experimental results demonstrate competitive performance with DNN compressors.
SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators
Authors: Karolis Martinkus, Andreas Loukas, Nathanaël Perraudin, Roger Wattenhofer
Date: 2022-04-04 00:00:00
Tasks: Graph Generation, Graph Matching

We approach the graph generation problem from a spectral perspective by first generating the dominant parts of the graph Laplacian spectrum and then building a graph matching these eigenvalues and eigenvectors. Spectral conditioning allows for direct modeling of the global and local graph structure and helps to overcome the expressivity and mode collapse issues of one-shot graph generators. Our novel GAN, called SPECTRE, enables the one-shot generation of much larger graphs than previously possible with one-shot models. SPECTRE outperforms state-of-the-art deep autoregressive generators in terms of modeling fidelity, while also avoiding expensive sequential generation and dependence on node ordering. A case in point, in sizable synthetic and real-world graphs SPECTRE achieves a 4-to-170 fold improvement over the best competitor that does not overfit and is 23-to-30 times faster than autoregressive generators.
Scalable Spike-and-Slab
Authors: Niloy Biswas, Lester Mackey, Xiao-Li Meng
Date: 2022-04-04 00:00:00
Tasks: Variable Selection

Spike-and-slab priors are commonly used for Bayesian variable selection, due to their interpretability and favorable statistical properties. However, existing samplers for spike-and-slab posteriors incur prohibitive computational costs when the number of variables is large. In this article, we propose Scalable Spike-and-Slab ($S^3$), a scalable Gibbs sampling implementation for high-dimensional Bayesian regression with the continuous spike-and-slab prior of George and McCulloch (1993). For a dataset with $n$ observations and $p$ covariates, $S^3$ has order $\max\{ n^2 p_t, np \}$ computational cost at iteration $t$ where $p_t$ never exceeds the number of covariates switching spike-and-slab states between iterations $t$ and $t-1$ of the Markov chain. This improves upon the order $n^2 p$ per-iteration cost of state-of-the-art implementations as, typically, $p_t$ is substantially smaller than $p$. We apply $S^3$ on synthetic and real-world datasets, demonstrating orders of magnitude speed-ups over existing exact samplers and significant gains in inferential quality over approximate samplers with comparable cost.
Cluster-based ensemble learning for wind power modeling with meteorological wind data
Authors: Hao Chen
Date: 2022-04-01 00:00:00
Tasks: Clustering, Ensemble Learning

Optimal implementation and monitoring of wind energy generation hinge on reliable power modeling that is vital for understanding turbine control, farm operational optimization, and grid load balance. Based on the idea of similar wind condition leads to similar wind power; this paper constructs a modeling scheme that orderly integrates three types of ensemble learning algorithms, bagging, boosting, and stacking, and clustering approaches to achieve optimal power modeling. It also investigates applications of different clustering algorithms and methodology for determining cluster numbers in wind power modeling. The results reveal that all ensemble models with clustering exploit the intrinsic information of wind data and thus outperform models without it by approximately 15% on average. The model with the best farthest first clustering is computationally rapid and performs exceptionally well with an improvement of around 30%. The modeling is further boosted by about 5% by introducing stacking that fuses ensembles with varying clusters. The proposed modeling framework thus demonstrates promise by delivering efficient and robust modeling performance.
Knowledge distillation with error-correcting transfer learning for wind power prediction
Authors: Hao Chen
Date: 2022-04-01 00:00:00
Tasks: Knowledge Distillation, Transfer Learning, Weather Forecasting

Wind power prediction, especially for turbines, is vital for the operation, controllability, and economy of electricity companies. Hybrid methodologies combining advanced data science with weather forecasting have been incrementally applied to the predictions. Nevertheless, individually modeling massive turbines from scratch and downscaling weather forecasts to turbine size are neither easy nor economical. Aiming at it, this paper proposes a novel framework with mathematical underpinnings for turbine power prediction. This framework is the first time to incorporate knowledge distillation into energy forecasting, enabling accurate and economical constructions of turbine models by learning knowledge from the well-established park model. Besides, park-scale weather forecasts non-explicitly are mapped to turbines by transfer learning of predicted power errors, achieving model correction for better performance. The proposed framework is deployed on five turbines featuring various terrains in an Arctic wind park, the results are evaluated against the competitors of ablation investigation. The major findings reveal that the proposed framework, developed on favorable knowledge distillation and transfer learning parameters tuning, yields performance boosts from 3.3 % to 23.9 % over its competitors. This advantage also exists in terms of wind energy physics and computing efficiency, which are verified by the prediction quality rate and calculation time.
Hysteresis-Based RL: Robustifying Reinforcement Learning-based Control Policies via Hybrid Control
Authors: Jan de Priester, Ricardo G. Sanfelice, Nathan van de Wouw
Date: 2022-04-01 00:00:00
Tasks: reinforcement-learning, Reinforcement Learning (RL)

Reinforcement learning (RL) is a promising approach for deriving control policies for complex systems. As we show in two control problems, the derived policies from using the Proximal Policy Optimization (PPO) and Deep Q-Network (DQN) algorithms may lack robustness guarantees. Motivated by these issues, we propose a new hybrid algorithm, which we call Hysteresis-Based RL (HyRL), augmenting an existing RL algorithm with hysteresis switching and two stages of learning. We illustrate its properties in two examples for which PPO and DQN fail.
Learnable latent embeddings for joint behavioral and neural analysis
Authors: Steffen Schneider, Jin Hwa Lee, Mackenzie Weygandt Mathis
Date: 2022-04-01 00:00:00

Mapping behavioral actions to neural activity is a fundamental goal of neuroscience. As our ability to record large neural and behavioral data increases, there is growing interest in modeling neural dynamics during adaptive behaviors to probe neural representations. In particular, neural latent embeddings can reveal underlying correlates of behavior, yet, we lack non-linear techniques that can explicitly and flexibly leverage joint behavior and neural data. Here, we fill this gap with a novel method, CEBRA, that jointly uses behavioral and neural data in a hypothesis- or discovery-driven manner to produce consistent, high-performance latent spaces. We validate its accuracy and demonstrate our tool's utility for both calcium and electrophysiology datasets, across sensory and motor tasks, and in simple or complex behaviors across species. It allows for single and multi-session datasets to be leveraged for hypothesis testing or can be used label-free. Lastly, we show that CEBRA can be used for the mapping of space, uncovering complex kinematic features, and rapid, high-accuracy decoding of natural movies from visual cortex.
Assimilation of Satellite Active Fires Data
Authors: James D. Haley
Date: 2022-04-01 00:00:00

Wildland fires pose an increasingly serious problem in our society. The number and severity of these fires has been rising for many years. Wildfires pose direct threats to life and property as well as threats through ancillary effects like reduced air quality. The aim of this thesis is to develop techniques to help combat the impacts of wildfires by improving wildfire modeling capabilities by using satellite fire observations. Already much work has been done in this direction by other researchers. Our work seeks to expand the body of knowledge using mathematically sound methods to utilize information about wildfires that considers the uncertainties inherent in the satellite data. In this thesis we explore methods for using satellite data to help initialize and steer wildfire simulations. In particular, we develop a method for constructing the history of a fire, a new technique for assimilating wildfire data, and a method for modifying the behavior of a modeled fire by inferring information about the fuels in the fire domain. These goals rely on being able to estimate the time a fire first arrived at every location in a geographic region of interest. Because detailed knowledge of real wildfires is typically unavailable, the basic procedure for developing and testing the methods in this thesis will be to first work with simulated data so that the estimates produced can be compared with known solutions. The methods thus developed are then applied to real-world scenarios. Analysis of these scenarios shows that the work with constructing the history of fires and data assimilation improves improves fire modeling capabilities. The research is significant because it gives us a better understanding of the capabilities and limitations of using satellite data to inform wildfire models and it points the way towards new avenues for modeling fire behavior.
Analysis of Sparse Subspace Clustering: Experiments and Random Projection
Authors: Mehmet F. Demirel, Enrico Au-Yeung
Date: 2022-04-01 00:00:00
Tasks: Clustering, Document Classification, Face Clustering, Image Segmentation, Semantic Segmentation

Clustering can be defined as the process of assembling objects into a number of groups whose elements are similar to each other in some manner. As a technique that is used in many domains, such as face clustering, plant categorization, image segmentation, document classification, clustering is considered one of the most important unsupervised learning problems. Scientists have surveyed this problem for years and developed different techniques that can solve it, such as k-means clustering. We analyze one of these techniques: a powerful clustering algorithm called Sparse Subspace Clustering. We demonstrate several experiments using this method and then introduce a new approach that can reduce the computational time required to perform sparse subspace clustering.
Revealing the CO2 emission reduction of ridesplitting and its determinants based on real-world data
Authors: Wenxiang Li, Yuanyuan Li, Ziyuan Pu, Long Cheng, Lei Wang, Linchuan Yang
Date: 2022-04-02 00:00:00
Tasks: Interpretable Machine Learning

Ridesplitting, which is a form of pooled ridesourcing service, has great potential to alleviate the negative impacts of ridesourcing on the environment. However, most existing studies only explored its theoretical environmental benefits based on optimization models and simulations. By contrast, this study aims to reveal the real-world emission reduction of ridesplitting and its determinants based on the observed data of ridesourcing in Chengdu, China. Integrating the trip data with the COPERT model, this study calculates the CO2 emissions of shared rides (ridesplitting) and their substituted single rides (regular ridesourcing) to estimate the CO2 emission reduction of each ridesplitting trip. The results show that not all ridesplitting trips reduce emissions from ridesourcing in the real world. The CO2 emission reduction rate of ridesplitting varies from trip to trip, averaging at 43.15g/km. Then, interpretable machine learning models, gradient boosting machines, are applied to explore the relationship between the CO2 emission reduction rate of ridesplitting and its determinants. Based on the SHapley Additive exPlanations (SHAP) method, the overlap rate and detour rate of shared rides are identified to be the most important factors that determine the CO2 emission reduction rate of ridesplitting. Increasing the overlap rate, the number of shared rides, average speed, and ride distance ratio while decreasing the detour rate, actual trip distance, and ride distance gap can increase the CO2 emission reduction rate of ridesplitting. In addition, nonlinear effects and interactions of the determinants are examined through the partial dependence plots. To sum up, this study provides a scientific method for the government and ridesourcing companies to better assess and optimize the environmental benefits of ridesplitting.