This study investigates the relationship between semi-supervised learning (SSL, which is training off partially labelled datasets) and open-set recognition (OSR, which is classification with simultaneous novelty detection) under the context of generative adversarial networks (GANs). Although no previous study has formally linked SSL and OSR, their respective methods share striking similarities. Specifically, SSL-GANs and OSR-GANs require their generators to produce 'bad-looking' samples which are used to regularise their classifier networks. We hypothesise that the definitions of bad-looking samples in SSL and OSR represents the same concept and realises the same goal. More formally, bad-looking samples lie in the complementary space, which is the area between and around the boundaries of the labelled categories within the classifier's embedding space. By regularising a classifier with samples in the complementary space, classifiers achieve improved generalisation for SSL and also generalise the open space for OSR. To test this hypothesis, we compare a foundational SSL-GAN with the state-of-the-art OSR-GAN under the same SSL-OSR experimental conditions. Our results find that SSL-GANs achieve near identical results to OSR-GANs, proving the SSL-OSR link. Subsequently, to further this new research path, we compare several SSL-GANs various SSL-OSR setups which this first benchmark results. A combined framework of SSL-OSR certainly improves the practicality and cost-efficiency of classifier training, and so further theoretical and application studies are also discussed.
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Sociodemographic inequalities in student achievement are a persistent concern for education systems and are increasingly recognized to be intersectional. Intersectionality considers the multidimensional nature of disadvantage, appreciating the interlocking social determinants which shape individual experience. Intersectional multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) is a new approach developed in population health but with limited application in educational research. In this study, we introduce and apply this approach to study sociodemographic inequalities in student achievement across two cohorts of students in London, England. We define 144 intersectional strata arising from combinations of student age, gender, free school meal status, special educational needs, and ethnicity. We find substantial strata-level variation in achievement composed primarily by additive rather than interactive effects with results stubbornly consistent across the cohorts. We conclude that policymakers should pay greater attention to multiply marginalized students and intersectional MAIHDA provides a useful approach to study their experiences.
A physics-informed convolutional neural network is proposed to simulate two phase flow in porous media with time-varying well controls. While most of PICNNs in existing literatures worked on parameter-to-state mapping, our proposed network parameterizes the solution with time-varying controls to establish a control-to-state regression. Firstly, finite volume scheme is adopted to discretize flow equations and formulate loss function that respects mass conservation laws. Neumann boundary conditions are seamlessly incorporated into the semi-discretized equations so no additional loss term is needed. The network architecture comprises two parallel U-Net structures, with network inputs being well controls and outputs being the system states. To capture the time-dependent relationship between inputs and outputs, the network is well designed to mimic discretized state space equations. We train the network progressively for every timestep, enabling it to simultaneously predict oil pressure and water saturation at each timestep. After training the network for one timestep, we leverage transfer learning techniques to expedite the training process for subsequent timestep. The proposed model is used to simulate oil-water porous flow scenarios with varying reservoir gridblocks and aspects including computation efficiency and accuracy are compared against corresponding numerical approaches. The results underscore the potential of PICNN in effectively simulating systems with numerous grid blocks, as computation time does not scale with model dimensionality. We assess the temporal error using 10 different testing controls with variation in magnitude and another 10 with higher alternation frequency with proposed control-to-state architecture. Our observations suggest the need for a more robust and reliable model when dealing with controls that exhibit significant variations in magnitude or frequency.
The beneficial role of noise in learning is nowadays a consolidated concept in the field of artificial neural networks, suggesting that even biological systems might take advantage of similar mechanisms to maximize their performance. The training-with-noise algorithm proposed by Gardner and collaborators is an emblematic example of a noise injection procedure in recurrent networks, which are usually employed to model real neural systems. We show how adding structure into noisy training data can substantially improve the algorithm performance, allowing to approach perfect classification and maximal basins of attraction. We also prove that the so-called Hebbian unlearning rule coincides with the training-with-noise algorithm when noise is maximal and data are fixed points of the network dynamics. A sampling scheme for optimal noisy data is eventually proposed and implemented to outperform both the training-with-noise and the Hebbian unlearning procedures.
Unlike primates, training artificial neural networks on changing data distributions leads to a rapid decrease in performance on old tasks. This phenomenon is commonly referred to as catastrophic forgetting. In this paper, we investigate the representational changes that underlie this performance decrease and identify three distinct processes that together account for the phenomenon. The largest component is a misalignment between hidden representations and readout layers. Misalignment occurs due to learning on additional tasks and causes internal representations to shift. Representational geometry is partially conserved under this misalignment and only a small part of the information is irrecoverably lost. All types of representational changes scale with the dimensionality of hidden representations. These insights have implications for deep learning applications that need to be continuously updated, but may also aid aligning ANN models to the rather robust biological vision.
In clinical trials of longitudinal continuous outcomes, reference based imputation (RBI) has commonly been applied to handle missing outcome data in settings where the estimand incorporates the effects of intercurrent events, e.g. treatment discontinuation. RBI was originally developed in the multiple imputation framework, however recently conditional mean imputation (CMI) combined with the jackknife estimator of the standard error was proposed as a way to obtain deterministic treatment effect estimates and correct frequentist inference. For both multiple and CMI, a mixed model for repeated measures (MMRM) is often used for the imputation model, but this can be computationally intensive to fit to multiple data sets (e.g. the jackknife samples) and lead to convergence issues with complex MMRM models with many parameters. Therefore, a step-wise approach based on sequential linear regression (SLR) of the outcomes at each visit was developed for the imputation model in the multiple imputation framework, but similar developments in the CMI framework are lacking. In this article, we fill this gap in the literature by proposing a SLR approach to implement RBI in the CMI framework, and justify its validity using theoretical results and simulations. We also illustrate our proposal on a real data application.
Electrical circuits are present in a variety of technologies, making their design an important part of computer aided engineering. The growing number of tunable parameters that affect the final design leads to a need for new approaches of quantifying their impact. Machine learning may play a key role in this regard, however current approaches often make suboptimal use of existing knowledge about the system at hand. In terms of circuits, their description via modified nodal analysis is well-understood. This particular formulation leads to systems of differential-algebraic equations (DAEs) which bring with them a number of peculiarities, e.g. hidden constraints that the solution needs to fulfill. We aim to use the recently introduced dissection concept for DAEs that can decouple a given system into ordinary differential equations, only depending on differential variables, and purely algebraic equations that describe the relations between differential and algebraic variables. The idea then is to only learn the differential variables and reconstruct the algebraic ones using the relations from the decoupling. This approach guarantees that the algebraic constraints are fulfilled up to the accuracy of the nonlinear system solver, which represents the main benefit highlighted in this article.
We propose a novel modular inference approach combining two different generative models -- generative adversarial networks (GAN) and normalizing flows -- to approximate the posterior distribution of physics-based Bayesian inverse problems framed in high-dimensional ambient spaces. We dub the proposed framework GAN-Flow. The proposed method leverages the intrinsic dimension reduction and superior sample generation capabilities of GANs to define a low-dimensional data-driven prior distribution. Once a trained GAN-prior is available, the inverse problem is solved entirely in the latent space of the GAN using variational Bayesian inference with normalizing flow-based variational distribution, which approximates low-dimensional posterior distribution by transforming realizations from the low-dimensional latent prior (Gaussian) to corresponding realizations of a low-dimensional variational posterior distribution. The trained GAN generator then maps realizations from this approximate posterior distribution in the latent space back to the high-dimensional ambient space. We also propose a two-stage training strategy for GAN-Flow wherein we train the two generative models sequentially. Thereafter, GAN-Flow can estimate the statistics of posterior-predictive quantities of interest at virtually no additional computational cost. The synergy between the two types of generative models allows us to overcome many challenges associated with the application of Bayesian inference to large-scale inverse problems, chief among which are describing an informative prior and sampling from the high-dimensional posterior. We demonstrate the efficacy and flexibility of GAN-Flow on various physics-based inverse problems of varying ambient dimensionality and prior knowledge using different types of GANs and normalizing flows.
Deep neural networks for graphs have emerged as a powerful tool for learning on complex non-euclidean data, which is becoming increasingly common for a variety of different applications. Yet, although their potential has been widely recognised in the machine learning community, graph learning is largely unexplored for downstream tasks such as robotics applications. To fully unlock their potential, hence, we propose a review of graph neural architectures from a robotics perspective. The paper covers the fundamentals of graph-based models, including their architecture, training procedures, and applications. It also discusses recent advancements and challenges that arise in applied settings, related for example to the integration of perception, decision-making, and control. Finally, the paper provides an extensive review of various robotic applications that benefit from learning on graph structures, such as bodies and contacts modelling, robotic manipulation, action recognition, fleet motion planning, and many more. This survey aims to provide readers with a thorough understanding of the capabilities and limitations of graph neural architectures in robotics, and to highlight potential avenues for future research.
We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized class of candidate models, the Fisher information of observed sequence probabilities lower-bounds the variance in model estimation from finite data. As sequence-length increases, the minimal variance scales as the square inverse of the length -- with constant coefficient given by the information rate. We discover a simple closed-form expression for this information rate, even in the case of infinite Markov order. We furthermore obtain the exact analytic lower bound on model variance from the observation-induced metadynamic among belief states. We discover ephemeral, exponential, and more general modes of convergence to the asymptotic information rate. Surprisingly, this myopic information rate converges to the asymptotic Fisher information rate with exactly the same relaxation timescales that appear in the myopic entropy rate as it converges to the Shannon entropy rate for the process. We illustrate these results with a sequence of examples that highlight qualitatively distinct features of stochastic processes that shape optimal learning.
Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.
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