pwc-archive/papers-with-abstracts huggingface dataset:
Sample-Efficient Optimisation with Probabilistic Transformer Surrogates
Authors: Alexandre Maraval, Matthieu Zimmer, Antoine Grosnit, Rasul Tutunov, Jun Wang, Haitham Bou Ammar
Date: 2022-05-27 00:00:00
Tasks: Bayesian Optimisation, Gaussian Processes

Faced with problems of increasing complexity, recent research in Bayesian Optimisation (BO) has focused on adapting deep probabilistic models as flexible alternatives to Gaussian Processes (GPs). In a similar vein, this paper investigates the feasibility of employing state-of-the-art probabilistic transformers in BO. Upon further investigation, we observe two drawbacks stemming from their training procedure and loss definition, hindering their direct deployment as proxies in black-box optimisation. First, we notice that these models are trained on uniformly distributed inputs, which impairs predictive accuracy on non-uniform data - a setting arising from any typical BO loop due to exploration-exploitation trade-offs. Second, we realise that training losses (e.g., cross-entropy) only asymptotically guarantee accurate posterior approximations, i.e., after arriving at the global optimum, which generally cannot be ensured. At the stationary points of the loss function, however, we observe a degradation in predictive performance especially in exploratory regions of the input space. To tackle these shortcomings we introduce two components: 1) a BO-tailored training prior supporting non-uniformly distributed points, and 2) a novel approximate posterior regulariser trading-off accuracy and input sensitivity to filter favourable stationary points for improved predictive performance. In a large panel of experiments, we demonstrate, for the first time, that one transformer pre-trained on data sampled from random GP priors produces competitive results on 16 benchmark black-boxes compared to GP-based BO. Since our model is only pre-trained once and used in all tasks without any retraining and/or fine-tuning, we report an order of magnitude time-reduction, while matching and sometimes outperforming GPs.
Bias Reduction via Cooperative Bargaining in Synthetic Graph Dataset Generation
Authors: Axel Wassington, Sergi Abadal
Date: 2022-05-27 00:00:00
Tasks: Benchmarking, Dataset Generation, Graph Neural Network, Selection bias

In general, to draw robust conclusions from a dataset, all the analyzed population must be represented on said dataset. Having a dataset that does not fulfill this condition normally leads to selection bias. Additionally, graphs have been used to model a wide variety of problems. Although synthetic graphs can be used to augment available real graph datasets to overcome selection bias, the generation of unbiased synthetic datasets is complex with current tools. In this work, we propose a method to find a synthetic graph dataset that has an even representation of graphs with different metrics. The resulting dataset can then be used, among others, for benchmarking graph processing techniques as the accuracy of different Graph Neural Network (GNN) models or the speedups obtained by different graph processing acceleration frameworks.
How Tempering Fixes Data Augmentation in Bayesian Neural Networks
Authors: Gregor Bachmann, Lorenzo Noci, Thomas Hofmann
Date: 2022-05-27 00:00:00
Tasks: Data Augmentation

While Bayesian neural networks (BNNs) provide a sound and principled alternative to standard neural networks, an artificial sharpening of the posterior usually needs to be applied to reach comparable performance. This is in stark contrast to theory, dictating that given an adequate prior and a well-specified model, the untempered Bayesian posterior should achieve optimal performance. Despite the community's extensive efforts, the observed gains in performance still remain disputed with several plausible causes pointing at its origin. While data augmentation has been empirically recognized as one of the main drivers of this effect, a theoretical account of its role, on the other hand, is largely missing. In this work we identify two interlaced factors concurrently influencing the strength of the cold posterior effect, namely the correlated nature of augmentations and the degree of invariance of the employed model to such transformations. By theoretically analyzing simplified settings, we prove that tempering implicitly reduces the misspecification arising from modeling augmentations as i.i.d. data. The temperature mimics the role of the effective sample size, reflecting the gain in information provided by the augmentations. We corroborate our theoretical findings with extensive empirical evaluations, scaling to realistic BNNs. By relying on the framework of group convolutions, we experiment with models of varying inherent degree of invariance, confirming its hypothesized relationship with the optimal temperature.
Transformers from an Optimization Perspective
Authors: Yongyi Yang, Zengfeng Huang, David Wipf
Date: 2022-05-27 00:00:00

Deep learning models such as the Transformer are often constructed by heuristics and experience. To provide a complementary foundation, in this work we study the following problem: Is it possible to find an energy function underlying the Transformer model, such that descent steps along this energy correspond with the Transformer forward pass? By finding such a function, we can view Transformers as the unfolding of an interpretable optimization process across iterations. This unfolding perspective has been frequently adopted in the past to elucidate more straightforward deep models such as MLPs and CNNs; however, it has thus far remained elusive obtaining a similar equivalence for more complex models with self-attention mechanisms like the Transformer. To this end, we first outline several major obstacles before providing companion techniques to at least partially address them, demonstrating for the first time a close association between energy function minimization and deep layers with self-attention. This interpretation contributes to our intuition and understanding of Transformers, while potentially laying the ground-work for new model designs.
Probabilistic Systems with Hidden State and Unobservable Transitions
Authors: Rebecca Bernemann, Barbara König, Matthias Schaffeld, Torben Weis
Date: 2022-05-27 00:00:00

We consider probabilistic systems with hidden state and unobservable transitions, an extension of Hidden Markov Models (HMMs) that in particular admits unobservable {\epsilon}-transitions (also called null transitions), allowing state changes of which the observer is unaware. Due to the presence of {\epsilon}-loops this additional feature complicates the theory and requires to carefully set up the corresponding probability space and random variables. In particular we present an algorithm for determining the most probable explanation given an observation (a generalization of the Viterbi algorithm for HMMs) and a method for parameter learning that adapts the probabilities of a given model based on an observation (a generalization of the Baum-Welch algorithm). The latter algorithm guarantees that the given observation has a higher (or equal) probability after adjustment of the parameters and its correctness can be derived directly from the so-called EM algorithm.
MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models
Authors: Erdun Gao, Ignavier Ng, Mingming Gong, Li Shen, Wei Huang, Tongliang Liu, Kun Zhang, Howard Bondell
Date: 2022-05-27 00:00:00
Tasks: Causal Discovery, Imputation, Inductive Bias

State-of-the-art causal discovery methods usually assume that the observational data is complete. However, the missing data problem is pervasive in many practical scenarios such as clinical trials, economics, and biology. One straightforward way to address the missing data problem is first to impute the data using off-the-shelf imputation methods and then apply existing causal discovery methods. However, such a two-step method may suffer from suboptimality, as the imputation algorithm may introduce bias for modeling the underlying data distribution. In this paper, we develop a general method, which we call MissDAG, to perform causal discovery from data with incomplete observations. Focusing mainly on the assumptions of ignorable missingness and the identifiable additive noise models (ANMs), MissDAG maximizes the expected likelihood of the visible part of observations under the expectation-maximization (EM) framework. In the E-step, in cases where computing the posterior distributions of parameters in closed-form is not feasible, Monte Carlo EM is leveraged to approximate the likelihood. In the M-step, MissDAG leverages the density transformation to model the noise distributions with simpler and specific formulations by virtue of the ANMs and uses a likelihood-based causal discovery algorithm with directed acyclic graph constraint. We demonstrate the flexibility of MissDAG for incorporating various causal discovery algorithms and its efficacy through extensive simulations and real data experiments.
Adaptive Random Forests for Energy-Efficient Inference on Microcontrollers
Authors: Francesco Daghero, Alessio Burrello, Chen Xie, Luca Benini, Andrea Calimera, Enrico Macii, Massimo Poncino, Daniele Jahier Pagliari
Date: 2022-05-27 00:00:00

Random Forests (RFs) are widely used Machine Learning models in low-power embedded devices, due to their hardware friendly operation and high accuracy on practically relevant tasks. The accuracy of a RF often increases with the number of internal weak learners (decision trees), but at the cost of a proportional increase in inference latency and energy consumption. Such costs can be mitigated considering that, in most applications, inputs are not all equally difficult to classify. Therefore, a large RF is often necessary only for (few) hard inputs, and wasteful for easier ones. In this work, we propose an early-stopping mechanism for RFs, which terminates the inference as soon as a high-enough classification confidence is reached, reducing the number of weak learners executed for easy inputs. The early-stopping confidence threshold can be controlled at runtime, in order to favor either energy saving or accuracy. We apply our method to three different embedded classification tasks, on a single-core RISC-V microcontroller, achieving an energy reduction from 38% to more than 90% with a drop of less than 0.5% in accuracy. We also show that our approach outperforms previous adaptive ML methods for RFs.
Feudal Multi-Agent Reinforcement Learning with Adaptive Network Partition for Traffic Signal Control
Authors: Jinming Ma, Feng Wu
Date: 2022-05-27 00:00:00
Tasks: Graph Neural Network, Multi-agent Reinforcement Learning, reinforcement-learning, Reinforcement Learning (RL), Traffic Signal Control

Multi-agent reinforcement learning (MARL) has been applied and shown great potential in multi-intersections traffic signal control, where multiple agents, one for each intersection, must cooperate together to optimize traffic flow. To encourage global cooperation, previous work partitions the traffic network into several regions and learns policies for agents in a feudal structure. However, static network partition fails to adapt to dynamic traffic flow, which will changes frequently over time. To address this, we propose a novel feudal MARL approach with adaptive network partition. Specifically, we first partition the network into several regions according to the traffic flow. To do this, we propose two approaches: one is directly to use graph neural network (GNN) to generate the network partition, and the other is to use Monte-Carlo tree search (MCTS) to find the best partition with criteria computed by GNN. Then, we design a variant of Qmix using GNN to handle various dimensions of input, given by the dynamic network partition. Finally, we use a feudal hierarchy to manage agents in each partition and promote global cooperation. By doing so, agents are able to adapt to the traffic flow as required in practice. We empirically evaluate our method both in a synthetic traffic grid and real-world traffic networks of three cities, widely used in the literature. Our experimental results confirm that our method can achieve better performance, in terms of average travel time and queue length, than several leading methods for traffic signal control.
Improving Bidding and Playing Strategies in the Trick-Taking game Wizard using Deep Q-Networks
Authors: Jonas Schumacher, Marco Pleines
Date: 2022-05-27 00:00:00
Tasks: Decision Making

In this work, the trick-taking game Wizard with a separate bidding and playing phase is modeled by two interleaved partially observable Markov decision processes (POMDP). Deep Q-Networks (DQN) are used to empower self-improving agents, which are capable of tackling the challenges of a highly non-stationary environment. To compare algorithms between each other, the accuracy between bid and trick count is monitored, which strongly correlates with the actual rewards and provides a well-defined upper and lower performance bound. The trained DQN agents achieve accuracies between 66% and 87% in self-play, leaving behind both a random baseline and a rule-based heuristic. The conducted analysis also reveals a strong information asymmetry concerning player positions during bidding. To overcome the missing Markov property of imperfect-information games, a long short-term memory (LSTM) network is implemented to integrate historic information into the decision-making process. Additionally, a forward-directed tree search is conducted by sampling a state of the environment and thereby turning the game into a perfect information setting. To our surprise, both approaches do not surpass the performance of the basic DQN agent.
Counterfactual Analysis in Dynamic Latent State Models
Authors: Martin Haugh, Raghav Singal
Date: 2022-05-27 00:00:00
Tasks: counterfactual, Epidemiology, Off-policy evaluation, State Space Models

We provide an optimization-based framework to perform counterfactual analysis in a dynamic model with hidden states. Our framework is grounded in the ``abduction, action, and prediction'' approach to answer counterfactual queries and handles two key challenges where (1) the states are hidden and (2) the model is dynamic. Recognizing the lack of knowledge on the underlying causal mechanism and the possibility of infinitely many such mechanisms, we optimize over this space and compute upper and lower bounds on the counterfactual quantity of interest. Our work brings together ideas from causality, state-space models, simulation, and optimization, and we apply it on a breast cancer case study. To the best of our knowledge, we are the first to compute lower and upper bounds on a counterfactual query in a dynamic latent-state model.
Error Bound of Empirical $\ell_2$ Risk Minimization for Noisy Standard and Generalized Phase Retrieval Problems
Authors: Junren Chen, Michael K. Ng
Date: 2022-05-27 00:00:00
Tasks: Retrieval

In this paper, we study the estimation performance of empirical $\ell_2$ risk minimization (ERM) in noisy (standard) phase retrieval (NPR) given by $y_k = |\alpha_k^*x_0|^2+\eta_k$, or noisy generalized phase retrieval (NGPR) formulated as $y_k = x_0^*A_kx_0 + \eta_k$, where $x_0\in\mathbb{K}^d$ is the desired signal, $n$ is the sample size, $\eta= (\eta_1,...,\eta_n)^\top$ is the noise vector. We establish new error bounds under different noise patterns, and our proofs are valid for both $\mathbb{K}=\mathbb{R}$ and $\mathbb{K}=\mathbb{C}$. In NPR under arbitrary noise vector $\eta$, we derive a new error bound $O\big(\|\eta\|_\infty\sqrt{\frac{d}{n}} + \frac{|\mathbf{1}^\top\eta|}{n}\big)$, which is tighter than the currently known one $O\big(\frac{\|\eta\|}{\sqrt{n}}\big)$ in many cases. In NGPR, we show $O\big(\|\eta\|\frac{\sqrt{d}}{n}\big)$ for arbitrary $\eta$. In both problems, the bounds for arbitrary noise immediately give rise to $\tilde{O}(\sqrt{\frac{d}{n}})$ for sub-Gaussian or sub-exponential random noise, with some conventional but inessential assumptions (e.g., independent or zero-mean condition) removed or weakened. In addition, we make a first attempt to ERM under heavy-tailed random noise assumed to have bounded $l$-th moment. To achieve a trade-off between bias and variance, we truncate the responses and propose a corresponding robust ERM estimator, which is shown to possess the guarantee $\tilde{O}\big(\big[\sqrt{\frac{d}{n}}\big]^{1-1/l}\big)$ in both NPR, NGPR. All the error bounds straightforwardly extend to the more general problems of rank-$r$ matrix recovery, and these results deliver a conclusion that the full-rank frame $\{A_k\}_{k=1}^n$ in NGPR is more robust to biased noise than the rank-1 frame $\{\alpha_k\alpha_k^*\}_{k=1}^n$ in NPR. Extensive experimental results are presented to illustrate our theoretical findings.
Multivariate Probabilistic Forecasting of Intraday Electricity Prices using Normalizing Flows
Authors: Eike Cramer, Dirk Witthaut, Alexander Mitsos, Manuel Dahmen
Date: 2022-05-27 00:00:00
Tasks: Density Estimation, Explainable artificial intelligence, Explainable Artificial Intelligence (XAI), Prediction Intervals, regression

Electricity is traded on various markets with different time horizons and regulations. Short-term intraday trading becomes increasingly important due to the higher penetration of renewables. In Germany, the intraday electricity price typically fluctuates around the day-ahead price of the European Power EXchange (EPEX) spot markets in a distinct hourly pattern. This work proposes a probabilistic modeling approach that models the intraday price difference to the day-ahead contracts. The model captures the emerging hourly pattern by considering the four 15 min intervals in each day-ahead price interval as a four-dimensional joint probability distribution. The resulting nontrivial, multivariate price difference distribution is learned using a normalizing flow, i.e., a deep generative model that combines conditional multivariate density estimation and probabilistic regression. Furthermore, this work discusses the influence of different external impact factors based on literature insights and impact analysis using explainable artificial intelligence (XAI). The normalizing flow is compared to an informed selection of historical data and probabilistic forecasts using a Gaussian copula and a Gaussian regression model. Among the different models, the normalizing flow identifies the trends with the highest accuracy and has the narrowest prediction intervals. Both the XAI analysis and the empirical experiments highlight that the immediate history of the price difference realization and the increments of the day-ahead price have the most substantial impact on the price difference.
Prune and distill: similar reformatting of image information along rat visual cortex and deep neural networks
Authors: Paolo Muratore, Sina Tafazoli, Eugenio Piasini, Alessandro Laio, Davide Zoccolan
Date: 2022-05-27 00:00:00
Tasks: Object, Object Recognition

Visual object recognition has been extensively studied in both neuroscience and computer vision. Recently, the most popular class of artificial systems for this task, deep convolutional neural networks (CNNs), has been shown to provide excellent models for its functional analogue in the brain, the ventral stream in visual cortex. This has prompted questions on what, if any, are the common principles underlying the reformatting of visual information as it flows through a CNN or the ventral stream. Here we consider some prominent statistical patterns that are known to exist in the internal representations of either CNNs or the visual cortex and look for them in the other system. We show that intrinsic dimensionality (ID) of object representations along the rat homologue of the ventral stream presents two distinct expansion-contraction phases, as previously shown for CNNs. Conversely, in CNNs, we show that training results in both distillation and active pruning (mirroring the increase in ID) of low- to middle-level image information in single units, as representations gain the ability to support invariant discrimination, in agreement with previous observations in rat visual cortex. Taken together, our findings suggest that CNNs and visual cortex share a similarly tight relationship between dimensionality expansion/reduction of object representations and reformatting of image information.
Global Convergence of Over-parameterized Deep Equilibrium Models
Authors: Zenan Ling, Xingyu Xie, Qiuhao Wang, Zongpeng Zhang, Zhouchen Lin
Date: 2022-05-27 00:00:00

A deep equilibrium model (DEQ) is implicitly defined through an equilibrium point of an infinite-depth weight-tied model with an input-injection. Instead of infinite computations, it solves an equilibrium point directly with root-finding and computes gradients with implicit differentiation. The training dynamics of over-parameterized DEQs are investigated in this study. By supposing a condition on the initial equilibrium point, we show that the unique equilibrium point always exists during the training process, and the gradient descent is proved to converge to a globally optimal solution at a linear convergence rate for the quadratic loss function. In order to show that the required initial condition is satisfied via mild over-parameterization, we perform a fine-grained analysis on random DEQs. We propose a novel probabilistic framework to overcome the technical difficulty in the non-asymptotic analysis of infinite-depth weight-tied models.
fakeWeather: Adversarial Attacks for Deep Neural Networks Emulating Weather Conditions on the Camera Lens of Autonomous Systems
Authors: Alberto Marchisio, Giovanni Caramia, Maurizio Martina, Muhammad Shafique
Date: 2022-05-27 00:00:00

Recently, Deep Neural Networks (DNNs) have achieved remarkable performances in many applications, while several studies have enhanced their vulnerabilities to malicious attacks. In this paper, we emulate the effects of natural weather conditions to introduce plausible perturbations that mislead the DNNs. By observing the effects of such atmospheric perturbations on the camera lenses, we model the patterns to create different masks that fake the effects of rain, snow, and hail. Even though the perturbations introduced by our attacks are visible, their presence remains unnoticed due to their association with natural events, which can be especially catastrophic for fully-autonomous and unmanned vehicles. We test our proposed fakeWeather attacks on multiple Convolutional Neural Network and Capsule Network models, and report noticeable accuracy drops in the presence of such adversarial perturbations. Our work introduces a new security threat for DNNs, which is especially severe for safety-critical applications and autonomous systems.