To understand the ability and limitations of convolutional neural networks to generate time series that mimic complex temporal signals, we trained a generative adversarial network consisting of deep convolutional networks to generate chaotic time series and used nonlinear time series analysis to evaluate the generated time series. A numerical measure of determinism and the Lyapunov exponent, a measure of trajectory instability, showed that the generated time series well reproduce the chaotic properties of the original time series. However, error distribution analyses showed that large errors appeared at a low but non-negligible rate. Such errors would not be expected if the distribution were assumed to be exponential.
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Renewed interest in the relationship between artificial and biological neural networks motivates the study of gradient-free methods. Considering the linear regression model with random design, we theoretically analyze in this work the biologically motivated (weight-perturbed) forward gradient scheme that is based on random linear combination of the gradient. If d denotes the number of parameters and k the number of samples, we prove that the mean squared error of this method converges for $k\gtrsim d^2\log(d)$ with rate $d^2\log(d)/k.$ Compared to the dimension dependence d for stochastic gradient descent, an additional factor $d\log(d)$ occurs.
Combinatorial and algebraic perspectives on the marginal independence structure of Bayesian networks
We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data in the form of an undirected graph called the unconditional dependence graph. We show that unconditional dependence graphs of Bayesian networks correspond to the graphs having equal independence and intersection numbers. Using this observation, a Gr\"obner basis for a toric ideal associated to unconditional dependence graphs of Bayesian networks is given and then extended by additional binomial relations to connect the space of all such graphs. An MCMC method, called GrUES (Gr\"obner-based Unconditional Equivalence Search), is implemented based on the resulting moves and applied to synthetic Gaussian data. GrUES recovers the true marginal independence structure via a penalized maximum likelihood or MAP estimate at a higher rate than simple independence tests while also yielding an estimate of the posterior, for which the $20\%$ HPD credible sets include the true structure at a high rate for data-generating graphs with density at least $0.5$.
Interpretability of neural networks and their underlying theoretical behavior remain an open field of study even after the great success of their practical applications, particularly with the emergence of deep learning. In this work, NN2Poly is proposed: a theoretical approach to obtain an explicit polynomial model that provides an accurate representation of an already trained fully-connected feed-forward artificial neural network (a multilayer perceptron or MLP). This approach extends a previous idea proposed in the literature, which was limited to single hidden layer networks, to work with arbitrarily deep MLPs in both regression and classification tasks. NN2Poly uses a Taylor expansion on the activation function, at each layer, and then applies several combinatorial properties to calculate the coefficients of the desired polynomials. Discussion is presented on the main computational challenges of this method, and the way to overcome them by imposing certain constraints during the training phase. Finally, simulation experiments as well as applications to real tabular data sets are presented to demonstrate the effectiveness of the proposed method.
The aim of this study was to develop a model to accurately identify corresponding points between organ segmentations of different patients for radiotherapy applications. A model for simultaneous correspondence and interpolation estimation in 3D shapes was trained with head and neck organ segmentations from planning CT scans. We then extended the original model to incorporate imaging information using two approaches: 1) extracting features directly from image patches, and 2) including the mean square error between patches as part of the loss function. The correspondence and interpolation performance were evaluated using the geodesic error, chamfer distance and conformal distortion metrics, as well as distances between anatomical landmarks. Each of the models produced significantly better correspondences than the baseline non-rigid registration approach. The original model performed similarly to the model with direct inclusion of image features. The best performing model configuration incorporated imaging information as part of the loss function which produced more anatomically plausible correspondences. We will use the best performing model to identify corresponding anatomical points on organs to improve spatial normalisation, an important step in outcome modelling, or as an initialisation for anatomically informed registrations. All our code is publicly available at //github.com/rrr-uom-projects/Unsup-RT-Corr-Net
Clustering of publication networks is an efficient way to obtain classifications of large collections of research publications. Such classifications can be used to, e.g., detect research topics, normalize citation relations, or explore the publication output of a unit. Citation networks can be created using a variety of approaches. Best practices to obtain classifications using clustering have been investigated, in particular the performance of different publication-publication relatedness measures. However, evaluation of different approaches to normalization of citation relations have not been explored to the same extent. In this paper, we evaluate five approaches to normalization of direct citation relations with respect to clustering solution quality in four data sets. A sixth approach is evaluated using no normalization. To assess the quality of clustering solutions, we use three measures. (1) We compare the clustering solution to the reference lists of a set of publications using the Adjusted Rand Index. (2) Using the Sihouette width measure, we quantity to which extent the publications have relations to other clusters than the one they have been assigned to. (3) We propose a measure that captures publications that have probably been inaccurately assigned. The results clearly show that normalization is preferred over unnormalized direct citation relations. Furthermore, the results indicate that the fractional normalization approach, which can be considered the standard approach, causes inaccurate assignments. The geometric normalization approach has a similar performance as the fractional approach regarding Adjusted Rand Index and Silhouette width but leads to fewer inaccurate assignments. We therefore believe that the geometric approach may be preferred over the fractional approach.
A problem related to the development of algorithms designed to find the structure of artificial neural network used for behavioural (black-box) modelling of selected dynamic processes has been addressed in this paper. The research has included four original proposals of algorithms dedicated to neural network architecture search. Algorithms have been based on well-known optimisation techniques such as evolutionary algorithms and gradient descent methods. In the presented research an artificial neural network of recurrent type has been used, whose architecture has been selected in an optimised way based on the above-mentioned algorithms. The optimality has been understood as achieving a trade-off between the size of the neural network and its accuracy in capturing the response of the mathematical model under which it has been learnt. During the optimisation, original specialised evolutionary operators have been proposed. The research involved an extended validation study based on data generated from a mathematical model of the fast processes occurring in a pressurised water nuclear reactor.
A linear-time algorithm for generating auxiliary subgraphs for the 3-edge-connected components of a connected multigraph is presented. The algorithm uses an innovative graph contraction operation and makes only one pass over the graph. By contrast, the previously best-known algorithms make multiple passes over the graph to decompose it into its 2-edge-connected components or 2-vertex-connected components, then its 3-edge-connected components or 3-vertex-connected components, and then construct a cactus representation for the 2-cuts to generate the auxiliary subgraphs for the 3-edge-connected components.
This study examines the efficacy of various neural network (NN) models in interpreting mental constructs via electroencephalogram (EEG) signals. Through the assessment of 16 prevalent NN models and their variants across four brain-computer interface (BCI) paradigms, we gauged their information representation capability. Rooted in comprehensive literature review findings, we proposed EEGNeX, a novel, purely ConvNet-based architecture. We pitted it against both existing cutting-edge strategies and the Mother of All BCI Benchmarks (MOABB) involving 11 distinct EEG motor imagination (MI) classification tasks and revealed that EEGNeX surpasses other state-of-the-art methods. Notably, it shows up to 2.1%-8.5% improvement in the classification accuracy in different scenarios with statistical significance (p < 0.05) compared to its competitors. This study not only provides deeper insights into designing efficient NN models for EEG data but also lays groundwork for future explorations into the relationship between bioelectric brain signals and NN architectures. For the benefit of broader scientific collaboration, we have made all benchmark models, including EEGNeX, publicly available at (//github.com/chenxiachan/EEGNeX).
To improve the robustness of transformer neural networks used for temporal-dynamics prediction of chaotic systems, we propose a novel attention mechanism called easy attention which we demonstrate in time-series reconstruction and prediction. As a consequence of the fact that self attention only makes useof the inner product of queries and keys, it is demonstrated that the keys, queries and softmax are not necessary for obtaining the attention score required to capture long-term dependencies in temporal sequences. Through implementing singular-value decomposition (SVD) on the softmax attention score, we further observe that the self attention compresses contribution from both queries and keys in the spanned space of the attention score. Therefore, our proposed easy-attention method directly treats the attention scores as learnable parameters. This approach produces excellent results when reconstructing and predicting the temporal dynamics of chaotic systems exhibiting more robustness and less complexity than the self attention or the widely-used long short-term memory (LSTM) network. Our results show great potential for applications in more complex high-dimensional dynamical systems. Keywords: Machine Learning, Transformer, Self Attention, Koopman Operator, Chaotic System.
Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.
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