pwc-archive/papers-with-abstracts huggingface dataset:
Graph Distillation with Eigenbasis Matching
Authors: Yang Liu, Deyu Bo, Chuan Shi
Date: 2023-10-13 00:00:00

The increasing amount of graph data places requirements on the efficient training of graph neural networks (GNNs). The emerging graph distillation (GD) tackles this challenge by distilling a small synthetic graph to replace the real large graph, ensuring GNNs trained on real and synthetic graphs exhibit comparable performance. However, existing methods rely on GNN-related information as supervision, including gradients, representations, and trajectories, which have two limitations. First, GNNs can affect the spectrum (i.e., eigenvalues) of the real graph, causing spectrum bias in the synthetic graph. Second, the variety of GNN architectures leads to the creation of different synthetic graphs, requiring traversal to obtain optimal performance. To tackle these issues, we propose Graph Distillation with Eigenbasis Matching (GDEM), which aligns the eigenbasis and node features of real and synthetic graphs. Meanwhile, it directly replicates the spectrum of the real graph and thus prevents the influence of GNNs. Moreover, we design a discrimination constraint to balance the effectiveness and generalization of GDEM. Theoretically, the synthetic graphs distilled by GDEM are restricted spectral approximations of the real graphs. Extensive experiments demonstrate that GDEM outperforms state-of-the-art GD methods with powerful cross-architecture generalization ability and significant distillation efficiency. Our code is available at https://github.com/liuyang-tian/GDEM.
A 4-approximation algorithm for min max correlation clustering
Authors: Holger Heidrich, Jannik Irmai, Bjoern Andres
Date: 2023-10-13 00:00:00
Tasks: Clustering

We introduce a lower bounding technique for the min max correlation clustering problem and, based on this technique, a combinatorial 4-approximation algorithm for complete graphs. This improves upon the previous best known approximation guarantees of 5, using a linear program formulation (Kalhan et al., 2019), and 40, for a combinatorial algorithm (Davies et al., 2023a). We extend this algorithm by a greedy joining heuristic and show empirically that it improves the state of the art in solution quality and runtime on several benchmark datasets.
Variational autoencoder with weighted samples for high-dimensional non-parametric adaptive importance sampling
Authors: Julien Demange-Chryst, François Bachoc, Jérôme Morio, Timothé Krauth
Date: 2023-10-13 00:00:00

Probability density function estimation with weighted samples is the main foundation of all adaptive importance sampling algorithms. Classically, a target distribution is approximated either by a non-parametric model or within a parametric family. However, these models suffer from the curse of dimensionality or from their lack of flexibility. In this contribution, we suggest to use as the approximating model a distribution parameterised by a variational autoencoder. We extend the existing framework to the case of weighted samples by introducing a new objective function. The flexibility of the obtained family of distributions makes it as expressive as a non-parametric model, and despite the very high number of parameters to estimate, this family is much more efficient in high dimension than the classical Gaussian or Gaussian mixture families. Moreover, in order to add flexibility to the model and to be able to learn multimodal distributions, we consider a learnable prior distribution for the variational autoencoder latent variables. We also introduce a new pre-training procedure for the variational autoencoder to find good starting weights of the neural networks to prevent as much as possible the posterior collapse phenomenon to happen. At last, we explicit how the resulting distribution can be combined with importance sampling, and we exploit the proposed procedure in existing adaptive importance sampling algorithms to draw points from a target distribution and to estimate a rare event probability in high dimension on two multimodal problems.
A Deep Neural Network -- Mechanistic Hybrid Model to Predict Pharmacokinetics in Rat
Authors: Florian Führer, Andrea Gruber, Holger Diedam, Andreas H. Göller, Stephan Menz, Sebastian Schneckener
Date: 2023-10-13 00:00:00

An important aspect in the development of small molecules as drugs or agro-chemicals is their systemic availability after intravenous and oral administration. The prediction of the systemic availability from the chemical structure of a potential candidate is highly desirable, as it allows to focus the drug or agrochemical development on compounds with a favorable kinetic profile. However, such pre-dictions are challenging as the availability is the result of the complex interplay between molecular properties, biology and physiology and training data is rare. In this work we improve the hybrid model developed earlier [1]. We reduce the median fold change error for the total oral exposure from 2.85 to 2.35 and for intravenous administration from 1.95 to 1.62. This is achieved by training on a larger data set, improving the neural network architecture as well as the parametrization of mechanistic model. Further, we extend our approach to predict additional endpoints and to handle different covariates, like sex and dosage form. In contrast to a pure machine learning model, our model is able to predict new end points on which it has not been trained. We demonstrate this feature by predicting the exposure over the first 24h, while the model has only been trained on the total exposure.
Jointly-Learned Exit and Inference for a Dynamic Neural Network : JEI-DNN
Authors: Florence Regol, Joud Chataoui, Mark Coates
Date: 2023-10-13 00:00:00
Tasks: Dynamic neural networks

Large pretrained models, coupled with fine-tuning, are slowly becoming established as the dominant architecture in machine learning. Even though these models offer impressive performance, their practical application is often limited by the prohibitive amount of resources required for every inference. Early-exiting dynamic neural networks (EDNN) circumvent this issue by allowing a model to make some of its predictions from intermediate layers (i.e., early-exit). Training an EDNN architecture is challenging as it consists of two intertwined components: the gating mechanism (GM) that controls early-exiting decisions and the intermediate inference modules (IMs) that perform inference from intermediate representations. As a result, most existing approaches rely on thresholding confidence metrics for the gating mechanism and strive to improve the underlying backbone network and the inference modules. Although successful, this approach has two fundamental shortcomings: 1) the GMs and the IMs are decoupled during training, leading to a train-test mismatch; and 2) the thresholding gating mechanism introduces a positive bias into the predictive probabilities, making it difficult to readily extract uncertainty information. We propose a novel architecture that connects these two modules. This leads to significant performance improvements on classification datasets and enables better uncertainty characterization capabilities.
The Computational Complexity of Finding Stationary Points in Non-Convex Optimization
Authors: Alexandros Hollender, Manolis Zampetakis
Date: 2023-10-13 00:00:00

Finding approximate stationary points, i.e., points where the gradient is approximately zero, of non-convex but smooth objective functions $f$ over unrestricted $d$-dimensional domains is one of the most fundamental problems in classical non-convex optimization. Nevertheless, the computational and query complexity of this problem are still not well understood when the dimension $d$ of the problem is independent of the approximation error. In this paper, we show the following computational and query complexity results: 1. The problem of finding approximate stationary points over unrestricted domains is PLS-complete. 2. For $d = 2$, we provide a zero-order algorithm for finding $\varepsilon$-approximate stationary points that requires at most $O(1/\varepsilon)$ value queries to the objective function. 3. We show that any algorithm needs at least $\Omega(1/\varepsilon)$ queries to the objective function and/or its gradient to find $\varepsilon$-approximate stationary points when $d=2$. Combined with the above, this characterizes the query complexity of this problem to be $\Theta(1/\varepsilon)$. 4. For $d = 2$, we provide a zero-order algorithm for finding $\varepsilon$-KKT points in constrained optimization problems that requires at most $O(1/\sqrt{\varepsilon})$ value queries to the objective function. This closes the gap between the works of Bubeck and Mikulincer [2020] and Vavasis [1993] and characterizes the query complexity of this problem to be $\Theta(1/\sqrt{\varepsilon})$. 5. Combining our results with the recent result of Fearnley et al. [2022], we show that finding approximate KKT points in constrained optimization is reducible to finding approximate stationary points in unconstrained optimization but the converse is impossible.
Wasserstein approximation schemes based on Voronoi partitions
Authors: Keaton Hamm, Varun Khurana
Date: 2023-10-13 00:00:00

We consider structured approximation of measures in Wasserstein space $\mathrm{W}_p(\mathbb{R}^d)$ for $p\in[1,\infty)$ using general measure approximants compactly supported on Voronoi regions derived from a scaled Voronoi partition of $\mathbb{R}^d$. We show that if a full rank lattice $\Lambda$ is scaled by a factor of $h\in(0,1]$, then approximation of a measure based on the Voronoi partition of $h\Lambda$ is $O(h)$ regardless of $d$ or $p$. We then use a covering argument to show that $N$-term approximations of compactly supported measures is $O(N^{-\frac1d})$ which matches known rates for optimal quantizers and empirical measure approximation in most instances. Additionally, we generalize our construction to nonuniform Voronoi partitions, highlighting the flexibility and robustness of our approach for various measure approximation scenarios. Finally, we extend these results to noncompactly supported measures with sufficient decay. Our findings are pertinent to applications in computer vision and machine learning where measures are used to represent structured data such as images.
Goodhart's Law in Reinforcement Learning
Authors: Jacek Karwowski, Oliver Hayman, Xingjian Bai, Klaus Kiendlhofer, Charlie Griffin, Joar Skalse
Date: 2023-10-13 00:00:00
Tasks: reinforcement-learning, Reinforcement Learning

Implementing a reward function that perfectly captures a complex task in the real world is impractical. As a result, it is often appropriate to think of the reward function as a proxy for the true objective rather than as its definition. We study this phenomenon through the lens of Goodhart's law, which predicts that increasing optimisation of an imperfect proxy beyond some critical point decreases performance on the true objective. First, we propose a way to quantify the magnitude of this effect and show empirically that optimising an imperfect proxy reward often leads to the behaviour predicted by Goodhart's law for a wide range of environments and reward functions. We then provide a geometric explanation for why Goodhart's law occurs in Markov decision processes. We use these theoretical insights to propose an optimal early stopping method that provably avoids the aforementioned pitfall and derive theoretical regret bounds for this method. Moreover, we derive a training method that maximises worst-case reward, for the setting where there is uncertainty about the true reward function. Finally, we evaluate our early stopping method experimentally. Our results support a foundation for a theoretically-principled study of reinforcement learning under reward misspecification.
Computing Marginal and Conditional Divergences between Decomposable Models with Applications
Authors: Loong Kuan Lee, Geoffrey I. Webb, Daniel F. Schmidt, Nico Piatkowski
Date: 2023-10-13 00:00:00

The ability to compute the exact divergence between two high-dimensional distributions is useful in many applications but doing so naively is intractable. Computing the alpha-beta divergence -- a family of divergences that includes the Kullback-Leibler divergence and Hellinger distance -- between the joint distribution of two decomposable models, i.e chordal Markov networks, can be done in time exponential in the treewidth of these models. However, reducing the dissimilarity between two high-dimensional objects to a single scalar value can be uninformative. Furthermore, in applications such as supervised learning, the divergence over a conditional distribution might be of more interest. Therefore, we propose an approach to compute the exact alpha-beta divergence between any marginal or conditional distribution of two decomposable models. Doing so tractably is non-trivial as we need to decompose the divergence between these distributions and therefore, require a decomposition over the marginal and conditional distributions of these models. Consequently, we provide such a decomposition and also extend existing work to compute the marginal and conditional alpha-beta divergence between these decompositions. We then show how our method can be used to analyze distributional changes by first applying it to a benchmark image dataset. Finally, based on our framework, we propose a novel way to quantify the error in contemporary superconducting quantum computers. Code for all experiments is available at: https://lklee.dev/pub/2023-icdm/code
On Generalization Bounds for Projective Clustering
Date: 2023-10-13 00:00:00
Proceeding: NeurIPS 2023 11
Tasks: Clustering, Generalization Bounds

Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the famous $k$-median and $k$-means objectives. One may also choose centers to be $j$ dimensional subspaces, which gives rise to subspace clustering. In this paper, we consider learning bounds for these problems. That is, given a set of $n$ samples $P$ drawn independently from some unknown, but fixed distribution $\mathcal{D}$, how quickly does a solution computed on $P$ converge to the optimal clustering of $\mathcal{D}$? We give several near optimal results. In particular, For center-based objectives, we show a convergence rate of $\tilde{O}\left(\sqrt{{k}/{n}}\right)$. This matches the known optimal bounds of [Fefferman, Mitter, and Narayanan, Journal of the Mathematical Society 2016] and [Bartlett, Linder, and Lugosi, IEEE Trans. Inf. Theory 1998] for $k$-means and extends it to other important objectives such as $k$-median. For subspace clustering with $j$-dimensional subspaces, we show a convergence rate of $\tilde{O}\left(\sqrt{\frac{kj^2}{n}}\right)$. These are the first provable bounds for most of these problems. For the specific case of projective clustering, which generalizes $k$-means, we show a convergence rate of $\Omega\left(\sqrt{\frac{kj}{n}}\right)$ is necessary, thereby proving that the bounds from [Fefferman, Mitter, and Narayanan, Journal of the Mathematical Society 2016] are essentially optimal.
Automatic Music Playlist Generation via Simulation-based Reinforcement Learning
Authors: Federico Tomasi, Joseph Cauteruccio, Surya Kanoria, Kamil Ciosek, Matteo Rinaldi, Zhenwen Dai
Date: 2023-10-13 00:00:00
Tasks: Collaborative Filtering, reinforcement-learning, Reinforcement Learning

Personalization of playlists is a common feature in music streaming services, but conventional techniques, such as collaborative filtering, rely on explicit assumptions regarding content quality to learn how to make recommendations. Such assumptions often result in misalignment between offline model objectives and online user satisfaction metrics. In this paper, we present a reinforcement learning framework that solves for such limitations by directly optimizing for user satisfaction metrics via the use of a simulated playlist-generation environment. Using this simulator we develop and train a modified Deep Q-Network, the action head DQN (AH-DQN), in a manner that addresses the challenges imposed by the large state and action space of our RL formulation. The resulting policy is capable of making recommendations from large and dynamic sets of candidate items with the expectation of maximizing consumption metrics. We analyze and evaluate agents offline via simulations that use environment models trained on both public and proprietary streaming datasets. We show how these agents lead to better user-satisfaction metrics compared to baseline methods during online A/B tests. Finally, we demonstrate that performance assessments produced from our simulator are strongly correlated with observed online metric results.
Online Relocating and Matching of Ride-Hailing Services: A Model-Based Modular Approach
Authors: Chang Gao, Xi Lin, Fang He, Xindi Tang
Date: 2023-10-13 00:00:00

This study proposes an innovative model-based modular approach (MMA) to dynamically optimize order matching and vehicle relocation in a ride-hailing platform. MMA utilizes a two-layer and modular modeling structure. The upper layer determines the spatial transfer patterns of vehicle flow within the system to maximize the total revenue of the current and future stages. With the guidance provided by the upper layer, the lower layer performs rapid vehicle-to-order matching and vehicle relocation. MMA is interpretable, and equipped with the customized and polynomial-time algorithm, which, as an online order-matching and vehicle-relocation algorithm, can scale past thousands of vehicles. We theoretically prove that the proposed algorithm can achieve the global optimum in stylized networks, while the numerical experiments based on both the toy network and realistic dataset demonstrate that MMA is capable of achieving superior systematic performance compared to batch matching and reinforcement-learning based methods. Moreover, its modular and lightweight modeling structure further enables it to achieve a high level of robustness against demand variation while maintaining a relatively low computational cost.
MINDE: Mutual Information Neural Diffusion Estimation
Authors: Giulio Franzese, Mustapha Bounoua, Pietro Michiardi
Date: 2023-10-13 00:00:00
Tasks: Mutual Information Estimation

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.
Federated Meta-Learning for Few-Shot Fault Diagnosis with Representation Encoding
Authors: Jixuan Cui, Jun Li, Zhen Mei, Kang Wei, Sha Wei, Ming Ding, Wen Chen, Song Guo
Date: 2023-10-13 00:00:00
Tasks: Diagnostic, Fault Diagnosis, Federated Learning, Meta-Learning, Out-of-Distribution Generalization

Deep learning-based fault diagnosis (FD) approaches require a large amount of training data, which are difficult to obtain since they are located across different entities. Federated learning (FL) enables multiple clients to collaboratively train a shared model with data privacy guaranteed. However, the domain discrepancy and data scarcity problems among clients deteriorate the performance of the global FL model. To tackle these issues, we propose a novel framework called representation encoding-based federated meta-learning (REFML) for few-shot FD. First, a novel training strategy based on representation encoding and meta-learning is developed. It harnesses the inherent heterogeneity among training clients, effectively transforming it into an advantage for out-of-distribution generalization on unseen working conditions or equipment types. Additionally, an adaptive interpolation method that calculates the optimal combination of local and global models as the initialization of local training is proposed. This helps to further utilize local information to mitigate the negative effects of domain discrepancy. As a result, high diagnostic accuracy can be achieved on unseen working conditions or equipment types with limited training data. Compared with the state-of-the-art methods, such as FedProx, the proposed REFML framework achieves an increase in accuracy by 2.17%-6.50% when tested on unseen working conditions of the same equipment type and 13.44%-18.33% when tested on totally unseen equipment types, respectively.
Measuring the Stability of Process Outcome Predictions in Online Settings
Authors: Suhwan Lee, Marco Comuzzi, Xixi Lu, Hajo A. Reijers
Date: 2023-10-13 00:00:00
Tasks: Decision Making, Predictive Process Monitoring, Time Series

Predictive Process Monitoring aims to forecast the future progress of process instances using historical event data. As predictive process monitoring is increasingly applied in online settings to enable timely interventions, evaluating the performance of the underlying models becomes crucial for ensuring their consistency and reliability over time. This is especially important in high risk business scenarios where incorrect predictions may have severe consequences. However, predictive models are currently usually evaluated using a single, aggregated value or a time-series visualization, which makes it challenging to assess their performance and, specifically, their stability over time. This paper proposes an evaluation framework for assessing the stability of models for online predictive process monitoring. The framework introduces four performance meta-measures: the frequency of significant performance drops, the magnitude of such drops, the recovery rate, and the volatility of performance. To validate this framework, we applied it to two artificial and two real-world event logs. The results demonstrate that these meta-measures facilitate the comparison and selection of predictive models for different risk-taking scenarios. Such insights are of particular value to enhance decision-making in dynamic business environments.