Robust Multi-Cellular Developmental Design

This paper introduces a continuous model for Multi-cellular Developmental Design. The cells are fixed on a 2D grid and exchange "chemicals" with their neighbors during the growth process. The quantity of chemicals that a cell produces, as well as the differentiation value of the cell in the phenotype, are controlled by a Neural Network (the genotype) that takes as inputs the chemicals produced by the neighboring cells at the previous time step. In the proposed model, the number of iterations of the growth process is not pre-determined, but emerges during evolution: only organisms for which the growth process stabilizes give a phenotype (the stable state), others are declared nonviable. The optimization of the controller is done using the NEAT algorithm, that optimizes both the topology and the weights of the Neural Networks. Though each cell only receives local information from its neighbors, the experimental results of the proposed approach on the 'flags' problems (the phenotype must match a given 2D pattern) are almost as good as those of a direct regression approach using the same model with global information. Moreover, the resulting multi-cellular organisms exhibit almost perfect self-healing characteristics

Distributed Multi-Agent Optimization with State-Dependent Communication

We study distributed algorithms for solving global optimization problems in which the objective function is the sum of local objective functions of agents and the constraint set is given by the intersection of local constraint sets of agents. We assume that each agent knows only his own local objective function and constraint set, and exchanges information with the other agents over a randomly varying network topology to update his information state. We assume a state-dependent communication model over this topology: communication is Markovian with respect to the states of the agents and the probability with which the links are available depends on the states of the agents. In this paper, we study a projected multi-agent subgradient algorithm under state-dependent communication. The algorithm involves each agent performing a local averaging to combine his estimate with the other agents' estimates, taking a subgradient step along his local objective function, and projecting the estimates on his local constraint set. The state-dependence of the communication introduces significant challenges and couples the study of information exchange with the analysis of subgradient steps and projection errors. We first show that the multi-agent subgradient algorithm when used with a constant stepsize may result in the agent estimates to diverge with probability one. Under some assumptions on the stepsize sequence, we provide convergence rate bounds on a "disagreement metric" between the agent estimates. Our bounds are time-nonhomogeneous in the sense that they depend on the initial starting time. Despite this, we show that agent estimates reach an almost sure consensus and converge to the same optimal solution of the global optimization problem with probability one under different assumptions on the local constraint sets and the stepsize sequence

Testing bounded arboricity

In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs with bounded treewidth) and randomly generated preferential attachment graphs. Graphs with bounded arboricity have been studied extensively in the past, in particular since for many problems they allow for much more efficient algorithms and/or better approximation ratios. We present a tolerant tester in the sparse-graphs model. The sparse-graphs model allows access to degree queries and neighbor queries, and the distance is defined with respect to the actual number of edges. More specifically, our algorithm distinguishes between graphs that are $\epsilon$-close to having arboricity $\alpha$ and graphs that $c \cdot \epsilon$-far from having arboricity $3\alpha$, where $c$ is an absolute small constant. The query complexity and running time of the algorithm are $\tilde{O}\left(\frac{n}{\sqrt{m}}\cdot \frac{\log(1/\epsilon)}{\epsilon} + \frac{n\cdot \alpha}{m} \cdot \left(\frac{1}{\epsilon}\right)^{O(\log(1/\epsilon))}\right)$ where $n$ denotes the number of vertices and $m$ denotes the number of edges. In terms of the dependence on $n$ and $m$ this bound is optimal up to poly-logarithmic factors since $\Omega(n/\sqrt{m})$ queries are necessary (and $\alpha = O(\sqrt{m}))$. We leave it as an open question whether the dependence on $1/\epsilon$ can be improved from quasi-polynomial to polynomial. Our techniques include an efficient local simulation for approximating the outcome of a global (almost) forest-decomposition algorithm as well as a tailored procedure of edge sampling

Is attention all you need in medical image analysis? A review

Medical imaging is a key component in clinical diagnosis, treatment planning and clinical trial design, accounting for almost 90% of all healthcare data. CNNs achieved performance gains in medical image analysis (MIA) over the last years. CNNs can efficiently model local pixel interactions and be trained on small-scale MI data. The main disadvantage of typical CNN models is that they ignore global pixel relationships within images, which limits their generalisation ability to understand out-of-distribution data with different 'global' information. The recent progress of Artificial Intelligence gave rise to Transformers, which can learn global relationships from data. However, full Transformer models need to be trained on large-scale data and involve tremendous computational complexity. Attention and Transformer compartments (Transf/Attention) which can well maintain properties for modelling global relationships, have been proposed as lighter alternatives of full Transformers. Recently, there is an increasing trend to co-pollinate complementary local-global properties from CNN and Transf/Attention architectures, which led to a new era of hybrid models. The past years have witnessed substantial growth in hybrid CNN-Transf/Attention models across diverse MIA problems. In this systematic review, we survey existing hybrid CNN-Transf/Attention models, review and unravel key architectural designs, analyse breakthroughs, and evaluate current and future opportunities as well as challenges. We also introduced a comprehensive analysis framework on generalisation opportunities of scientific and clinical impact, based on which new data-driven domain generalisation and adaptation methods can be stimulated

Stochastic expectation propagation

Expectation propagation (EP) is a deterministic approximation algorithm that is often used to perform approximate Bayesian parameter learning. EP approximates the full intractable posterior distribution through a set of local approximations that are iteratively refined for each datapoint. EP can offer analytic and computational advantages over other approximations, such as Variational Inference (VI), and is the method of choice for a number of models. The local nature of EP appears to make it an ideal candidate for performing Bayesian learning on large models in large-scale dataset settings. However, EP has a crucial limitation in this context: the number of approximating factors needs to increase with the number of data-points, N, which often entails a prohibitively large memory overhead. This paper presents an extension to EP, called stochastic expectation propagation (SEP), that maintains a global posterior approximation (like VI) but updates it in a local way (like EP). Experiments on a number of canonical learning problems using synthetic and real-world datasets indicate that SEP performs almost as well as full EP, but reduces the memory consumption by a factor of $N$. SEP is therefore ideally suited to performing approximate Bayesian learning in the large model, large dataset setting

On robust estimation of low-frequency variability trends in discrete Markovian sequences of atmospheric circulation patterns

Identification and analysis of temporal trends and low-frequency variability in discrete time series is an important practical topic in understanding and predic- tion of many atmospheric processes, for example, in analysis of climate change. Widely used numerical techniques of trend identification (like local Gaussian ker- nel smoothing) impose some strong mathematical assumptions on the analyzed data and are not robust to model sensitivity. The latter becomes crucial when analyzing historical observation data with a short record. Two global robust nu- merical methods for the trend estimation in discrete non-stationary Markovian data based on different sets of implicit mathematical assumptions are introduced and compared here. The methods are first compared on a simple model exam- ple, the importance of mathematical assumptions on the data is explained and numerical problems of local Gaussian kernel smoothing are demonstrated. Pre- sented methods are applied to analysis of the historical sequence of atmospheric circulation patterns over UK between 1946-2007. It is demonstrated that the influence of the seasonal pattern variability on transition processes is dominated by the long-term effects revealed by the introduced methods. Despite of the dif- ferences in the mathematical assumptions implied by both presented methods, almost identical symmetrical changes of the cyclonic and anticyclonic pattern probabilities are identified in the analyzed data, with the confidence intervals being smaller then in the case of the local Gaussian kernel smoothing algorithm. Analysis results are investigated with respect to model sensitivity and compared to standard analysis technique based on a local Gaussian kernel smoothing. Finally, the implications of the discussed strategies on long-range predictability of the data-fitted Markovian models are discussed

From Symmetry to Geometry: Tractable Nonconvex Problems

As science and engineering have become increasingly data-driven, the role of optimization has expanded to touch almost every stage of the data analysis pipeline, from the signal and data acquisition to modeling and prediction. The optimization problems encountered in practice are often nonconvex. While challenges vary from problem to problem, one common source of nonconvexity is nonlinearity in the data or measurement model. Nonlinear models often exhibit symmetries, creating complicated, nonconvex objective landscapes, with multiple equivalent solutions. Nevertheless, simple methods (e.g., gradient descent) often perform surprisingly well in practice. The goal of this survey is to highlight a class of tractable nonconvex problems, which can be understood through the lens of symmetries. These problems exhibit a characteristic geometric structure: local minimizers are symmetric copies of a single "ground truth" solution, while other critical points occur at balanced superpositions of symmetric copies of the ground truth, and exhibit negative curvature in directions that break the symmetry. This structure enables efficient methods to obtain global minimizers. We discuss examples of this phenomenon arising from a wide range of problems in imaging, signal processing, and data analysis. We highlight the key role of symmetry in shaping the objective landscape and discuss the different roles of rotational and discrete symmetries. This area is rich with observed phenomena and open problems; we close by highlighting directions for future research.Comment: review paper submitted to SIAM Review, 34 pages, 10 figure

Explanations Based on Item Response Theory (eXirt): A Model-Specific Method to Explain Tree-Ensemble Model in Trust Perspective

In recent years, XAI researchers have been formalizing proposals and developing new methods to explain black box models, with no general consensus in the community on which method to use to explain these models, with this choice being almost directly linked to the popularity of a specific method. Methods such as Ciu, Dalex, Eli5, Lofo, Shap and Skater emerged with the proposal to explain black box models through global rankings of feature relevance, which based on different methodologies, generate global explanations that indicate how the model's inputs explain its predictions. In this context, 41 datasets, 4 tree-ensemble algorithms (Light Gradient Boosting, CatBoost, Random Forest, and Gradient Boosting), and 6 XAI methods were used to support the launch of a new XAI method, called eXirt, based on Item Response Theory - IRT and aimed at tree-ensemble black box models that use tabular data referring to binary classification problems. In the first set of analyses, the 164 global feature relevance ranks of the eXirt were compared with 984 ranks of the other XAI methods present in the literature, seeking to highlight their similarities and differences. In a second analysis, exclusive explanations of the eXirt based on Explanation-by-example were presented that help in understanding the model trust. Thus, it was verified that eXirt is able to generate global explanations of tree-ensemble models and also local explanations of instances of models through IRT, showing how this consolidated theory can be used in machine learning in order to obtain explainable and reliable models.Comment: 54 pages, 15 Figures, 3 Equations, 7 tabl

Efficient evolutionary algorithms for optimal control

If optimal control problems are solved by means of gradient based local search methods, convergence to local solutions is likely. Recently, there has been an increasing interest in the use of global optimisation algorithms to solve optimal control problems, which are expected to have local solutions. Evolutionary Algorithms (EAs) are global optimisation algorithms that have mainly been applied to solve static optimisation problems. Only rarely Evolutionary Algorithms have been used to solve optimal control problems. This may be due to the belief that their computational efficiency is insufficient to solve this type of problems. In addition, the application of Evolutionary Algorithms is a relatively young area of research. As demonstrated in this thesis, Evolutionary Algorithms exist which have significant advantages over other global optimisation methods for optimal control, while their efficiency is comparable.The purpose of this study was to investigate and search for efficient evolutionary algorithms to solve optimal control problems that are expected to have local solutions. These optimal control problems are called multi-modal. An important additional requirement for the practical application of these algorithms is that they preferably should not require any algorithm parameter tuning. Therefore algorithms with less algorithm parameters should be preferred. In addition guidelines for the choice of algorithm parameter values, and the possible development of automatic algorithm parameter adjustment strategies, are important issues.This study revealed that Differential Evolution (DE) algorithms are a class of evolutionary algorithms that do not share several theoretical and practical limitations that other Genetic Algorithms have. As a result they are significantly more efficient than other Genetic Algorithms, such as Breeder Genetic Algorithms (BGA), when applied to multi-modal optimal control problems. Their efficiency is comparable to the efficiency of Iterative Dynamic Programming (IDP), a global optimisation approach specifically designed for optimal control. Moreover the DE algorithms turned out to be significantly less sensitive to problems concerning the selection or tuning of algorithm parameters and the initialisation of the algorithm.Although it is not a DE algorithm, the GENOCOP algorithm is considered to be one of the most efficient genetic algorithms with real-valued individuals and specialized evolutionary operators. This algorithm was the starting point of our research. In Chapter 2 it was applied to some optimal control problems from chemical engineering. These problems were high dimensional, non-linear, multivariable, multi-modal and non-differentiable. Basically with GENOCOP the same solutions were obtained as with Iterative Dynamic Programming. Moreover GENOCOP is more successful in locating the global solution in comparison with other local optimisation algorithms. GENOCOP'S efficiency however is rather poor and the algorithm parameter tuning rather complicated. This motivated us to seek for more efficient evolutionary algorithms.Mathematical arguments found in the literature state that DE algorithms outperform other Evolutionary Algorithms in terms of computational efficiency. Therefore in Chapter 3, DE algorithms, generally used to solve continuous parameter optimisation problems, were used to solve two multi-modal (benchmark) optimal control problems. Also some Breeder Genetic Algorithms (BGA) were applied to solve these problems. The results obtained with these algorithms were compared to one another, and to the results obtained with IDP. The comparison confirmed that DE algorithms stand out in terms of efficiency as compared to the Breeder Genetic algorithms. Moreover, in contrast to the majority of Evolutionary Algorithms, which have many algorithm parameters that need to be selected or tuned, DE has only three algorithm parameters that have to be selected or tuned. These are the population size (µ), the crossover constant (CR) and the differential variation amplification (F). The population size plays a crucial role in solving multi-modal optimal control problems. Selecting a smaller population size enhances the computational efficiency but reduces the probability of finding the global solution. During our investigations we tried to find the best trade-off. One of the most efficient DE algorithms is denoted by DE/best/2/bin . All the investigated DE algorithms solved the two benchmark multi-modal optimal control problems properly and efficiently. The computational efficiency achieved by the DE algorithms in solving the first low multi-modal problem, was comparable to that of IDP. When applied to the second highly multi-modal problem, the computational efficiency of DE was slightly inferior to the one of IDP, after tuning of the algorithm parameters. However, the selection or tuning of the algorithm parameters for IDP is more difficult and more involved.From our investigation the following guidelines were obtained for the selection of the DE algorithm parameters. Take the population size less than or equal to two times the number of variables to be optimised that result from the control parameterisation of the original optimal control problem ( µ ≤ 2n u ). Highly multi-modal optimal control problems require a large value of the differential variation amplification ( F ≥0.9) and a very small or zero value for the crossover constant (0≤ CR ≤0.2). Low multi-modal optimal control problems need a medium value for the differential variation amplification (0.4≤ CR ≤0.6) and a large or medium value for the crossover constant (0.2≤ CR ≤0.5). In contrast to IDP, finding near-optimal values for the algorithm parameters is very simple for DE algorithms.Generally, the DE algorithm parameters are kept constant during the optimization process. A more effective and efficient algorithm may be obtained if they are adjusted on-line. In Chapter 4, a strategy that on-line adjusts the differential variation amplification ( F ) and the crossover constant ( CR ) using a measure of the diversity of the individuals in the population, was proposed. Roughly, the proposed strategy takes large values for F and small values for CR at the beginning of the optimization in order to promote a global search. When the population approaches the solution, F is decreased in order to promote a local search, and the crossover parameter CR is enlarged to increase the speed of convergence. When implemented on the DE algorithm DE/rand/1/bin and applied to the two benchmark multi-modal optimal control problems, the computational efficiency significantly improved and also the probability of locating the global solution.To judge the opportunities and advantages of using Evolutionary Algorithms to solve problems related to optimal control, in Chapter 5 several engineering applications concerning optimal greenhouse cultivation control are considered. In Chapter 5.1 genetic algorithms with binary individuals (Simple Genetic Algorithm) and floating-point representation (GENOCOP) for the individuals are used to estimate some of the parameters of a two-state dynamic model of a lettuce crop, the so-called NICOLET model. This model is intended to predict dry weight and nitrate content of lettuce at harvest time. Parameter estimation problems usually suffer from local minima. This study showed that Evolutionary Algorithms are suitable to calibrate the parameters of a dynamic model. However the required computation time is significant. Partly this is due to the high computational load of a single objective function evaluation, which for parameter optimisation problems involves a system simulation. Even though parameter optimisation is very often performed off-line, thus making computation time perhaps less important, more efficient evolutionary algorithms like DE are to be preferred.In Chapter 5.2 an optimal control problem of nitrate concentration in a lettuce crop was solved by means of two different algorithms. The ACW (Adjustable Control-variation Weight) gradient algorithm, which searches for local solutions, and the DE algorithm DE/best/2/bin that searches for a global solution. The dynamic system is a modified two-state dynamic model of a lettuce crop (NICOLET B3) and the control problem has a fixed final time and control and terminal state constraints. The DE algorithm was extended in order to deal with this.The results showed that this problem probably does not have local solutions and that the control parameterisation required by the DE algorithm causes some difficulties in accurately approximating the continuous solution obtained by the ACW algorithm. On the other hand the computational efficiency of the evolutionary algorithm turned out to be impressive. An almost natural conclusion therefore is to combine a DE algorithm with a gradient algorithm.In Chapter 5.3 the combination of a DE algorithm and a first order gradient algorithm is used to solve an optimal control problem. The DE algorithm is used to approximate the global solution sufficiently close after which the gradient algorithm can converge to it efficiently. This approach was successfully tried on the optimal control of nitrate in lettuce, which unfortunately in this case, seems to have no local solutions. Still the feasibility of this approach, which is important for all types of optimal control problems of which it is unknown a-priori whether they have local solutions, was clearly demonstrated.Finally, in Chapter six this thesis ends with an overall discussion, conclusions and suggestions for future research