The Symmetric Information Bottleneck (SIB), an extension of the more familiar Information Bottleneck, is a dimensionality reduction technique that simultaneously compresses two random variables to preserve information between their compressed versions. We introduce the Generalized Symmetric Information Bottleneck (GSIB), which explores different functional forms of the cost of such simultaneous reduction. We then explore the dataset size requirements of such simultaneous compression. We do this by deriving bounds and root-mean-squared estimates of statistical fluctuations of the involved loss functions. We show that, in typical situations, the simultaneous GSIB compression requires qualitatively less data to achieve the same errors compared to compressing variables one at a time. We suggest that this is an example of a more general principle that simultaneous compression is more data efficient than independent compression of each of the input variables.
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Neural Networks
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Neural networks (NNs) are primarily developed within the frequentist statistical framework. Nevertheless, frequentist NNs lack the capability to provide uncertainties in the predictions, and hence their robustness can not be adequately assessed. Conversely, the Bayesian neural networks (BNNs) naturally offer predictive uncertainty by applying Bayes' theorem. However, their computational requirements pose significant challenges. Moreover, both frequentist NNs and BNNs suffer from overfitting issues when dealing with noisy and sparse data, which render their predictions unwieldy away from the available data space. To address both these problems simultaneously, we leverage insights from a hierarchical setting in which the parameter priors are conditional on hyperparameters to construct a BNN by applying a semi-analytical framework known as nonlinear sparse Bayesian learning (NSBL). We call our network sparse Bayesian neural network (SBNN) which aims to address the practical and computational issues associated with BNNs. Simultaneously, imposing a sparsity-inducing prior encourages the automatic pruning of redundant parameters based on the automatic relevance determination (ARD) concept. This process involves removing redundant parameters by optimally selecting the precision of the parameters prior probability density functions (pdfs), resulting in a tractable treatment for overfitting. To demonstrate the benefits of the SBNN algorithm, the study presents an illustrative regression problem and compares the results of a BNN using standard Bayesian inference, hierarchical Bayesian inference, and a BNN equipped with the proposed algorithm. Subsequently, we demonstrate the importance of considering the full parameter posterior by comparing the results with those obtained using the Laplace approximation with and without NSBL.
Trust is essential for our interactions with others but also with artificial intelligence (AI) based systems. To understand whether a user trusts an AI, researchers need reliable measurement tools. However, currently discussed markers mostly rely on expensive and invasive sensors, like electroencephalograms, which may cause discomfort. The analysis of mouse trajectory has been suggested as a convenient tool for trust assessment. However, the relationship between trust, confidence and mouse trajectory is not yet fully understood. To provide more insights into this relationship, we asked participants (n = 146) to rate whether several tweets were offensive while an AI suggested its assessment. Our results reveal which aspects of the mouse trajectory are affected by the users subjective trust and confidence ratings; yet they indicate that these measures might not explain sufficiently the variance to be used on their own. This work examines a potential low-cost trust assessment in AI systems.
We present our submission to the BabyLM challenge, whose goal was to improve the sample efficiency of language models. We trained an ensemble consisting of a GPT-2 and small LLaMA models on the developmentally-plausible, 10M-word BabyLM dataset, then distilled it into a small, 58M-parameter LLaMA model, which exceeds in performance both of its teachers as well as a similar model trained without distillation. This suggests that distillation can not only retain the full performance of the teacher model when the latter is trained on a sufficiently small dataset; it can exceed it, and lead to significantly better performance than direct training.
The Flexible Job Shop Scheduling Problem (FJSSP) has been extensively studied in the literature, and multiple approaches have been proposed within the heuristic, exact, and metaheuristic methods. However, the industry's demand to be able to respond in real-time to disruptive events has generated the necessity to be able to generate new schedules within a few seconds. Among these methods, under this constraint, only dispatching rules (DRs) are capable of generating schedules, even though their quality can be improved. To improve the results, recent methods have been proposed for modeling the FJSSP as a Markov Decision Process (MDP) and employing reinforcement learning to create a policy that generates an optimal solution assigning operations to machines. Nonetheless, there is still room for improvement, particularly in the larger FJSSP instances which are common in real-world scenarios. Therefore, the objective of this paper is to propose a method capable of robustly solving large instances of the FJSSP. To achieve this, we propose a novel way of modeling the FJSSP as an MDP using graph neural networks. We also present two methods to make inference more robust: generating a diverse set of scheduling policies that can be parallelized and limiting them using DRs. We have tested our approach on synthetically generated instances and various public benchmarks and found that our approach outperforms dispatching rules and achieves better results than three other recent deep reinforcement learning methods on larger FJSSP instances.
This article establishes novel strong uniform laws of large numbers for randomly weighted sums such as bootstrap means. By leveraging recent advances, these results extend previous work in their general applicability to a wide range of weighting procedures and in their flexibility with respect to the effective bootstrap sample size. In addition to the standard multinomial bootstrap and the m-out-of-n bootstrap, our results apply to a large class of randomly weighted sums involving negatively orthant dependent (NOD) weights, including the Bayesian bootstrap, jackknife, resampling without replacement, simple random sampling with over-replacement, independent weights, and multivariate Gaussian weighting schemes. Weights are permitted to be non-identically distributed and possibly even negative. Our proof technique is based on extending a proof of the i.i.d. strong uniform law of large numbers to employ strong laws for randomly weighted sums; in particular, we exploit a recent Marcinkiewicz--Zygmund strong law for NOD weighted sums.
This paper presents a novel approach to solving the Flying Sidekick Travelling Salesman Problem (FSTSP) using a state-of-the-art self-adaptive genetic algorithm. The Flying Sidekick Travelling Salesman Problem is a combinatorial optimisation problem that extends the Travelling Salesman Problem (TSP) by introducing the use of drones. In FSTSP, the objective is to minimise the total time to visit all locations while strategically deploying a drone to serve hard-to-reach customer locations. Also, to the best of my knowledge, this is the first time a self-adaptive genetic algorithm (GA) has been used to solve the FSTSP problem. Experimental results on smaller-sized problem instances demonstrate that this algorithm can find a higher quantity of optimal solutions and a lower percentage gap to the optimal solution compared to rival algorithms. Moreover, on larger-sized problem instances, this algorithm outperforms all rival algorithms on each problem size while maintaining a reasonably low computation time.
Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article, the Modulated Fourier Expansion is analytically derived for a linear partial differential equation with a multifrequency highly oscillatory potential. The solution of the equation is expressed as a convergent Neumann series within the appropriate Sobolev space. The proposed approach enables, firstly, to derive a general formula for the error associated with the approximation of the solution by MFE, and secondly, to determine the coefficients for this expansion -- without the need to solve numerically the system of differential equations to find the coefficients of MFE. Numerical experiments illustrate the theoretical investigations.
Randomized Controlled Trials (RCTs) may suffer from limited scope. In particular, samples may be unrepresentative: some RCTs over- or under- sample individuals with certain characteristics compared to the target population, for which one wants conclusions on treatment effectiveness. Re-weighting trial individuals to match the target population can improve the treatment effect estimation. In this work, we establish the exact expressions of the bias and variance of such reweighting procedures -- also called Inverse Propensity of Sampling Weighting (IPSW) -- in presence of categorical covariates for any sample size. Such results allow us to compare the theoretical performance of different versions of IPSW estimates. Besides, our results show how the performance (bias, variance, and quadratic risk) of IPSW estimates depends on the two sample sizes (RCT and target population). A by-product of our work is the proof of consistency of IPSW estimates. Results also reveal that IPSW performances are improved when the trial probability to be treated is estimated (rather than using its oracle counterpart). In addition, we study choice of variables: how including covariates that are not necessary for identifiability of the causal effect may impact the asymptotic variance. Including covariates that are shifted between the two samples but not treatment effect modifiers increases the variance while non-shifted but treatment effect modifiers do not. We illustrate all the takeaways in a didactic example, and on a semi-synthetic simulation inspired from critical care medicine.
Reservoir Computing (RC) is a type of recursive neural network (RNN), and there can be no doubt that the RC will be more and more widely used for building future prediction models for time-series data, with low training cost, high speed and high computational power. However, research into the mathematical structure of RC neural networks has only recently begun. Bollt (2021) clarified the necessity of the autoregressive (AR) model for gaining the insight into the mathematical structure of RC neural networks, and indicated that the Wold decomposition theorem is the milestone for understanding of these. Keeping this celebrated result in mind, in this paper, we clarify hidden structures of input and recurrent weight matrices in RC neural networks, and show that such structures attain perfect prediction for the AR type of time series data.
Within the rapidly developing Internet of Things (IoT), numerous and diverse physical devices, Edge devices, Cloud infrastructure, and their quality of service requirements (QoS), need to be represented within a unified specification in order to enable rapid IoT application development, monitoring, and dynamic reconfiguration. But heterogeneities among different configuration knowledge representation models pose limitations for acquisition, discovery and curation of configuration knowledge for coordinated IoT applications. This paper proposes a unified data model to represent IoT resource configuration knowledge artifacts. It also proposes IoT-CANE (Context-Aware recommendatioN systEm) to facilitate incremental knowledge acquisition and declarative context driven knowledge recommendation.
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