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In fitting data with a spline, finding the optimal placement of knots can significantly improve the quality of the fit. However, the challenging high-dimensional and non-convex optimization problem associated with completely free knot placement has been a major roadblock in using this approach. We present a method that uses particle swarm optimization (PSO) combined with model selection to address this challenge. The problem of overfitting due to knot clustering that accompanies free knot placement is mitigated in this method by explicit regularization, resulting in a significantly improved performance on highly noisy data. The principal design choices available in the method are delineated and a statistically rigorous study of their effect on performance is carried out using simulated data and a wide variety of benchmark functions. Our results demonstrate that PSO-based free knot placement leads to a viable and flexible adaptive spline fitting approach that allows the fitting of both smooth and non-smooth functions.
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We develop a fully Bayesian nonparametric regression model based on a Levy process prior named MLABS (Multivariate Levy Adaptive B-Spline regression) model, a multivariate version of the LARK (Levy Adaptive Regression Kernels) models, for estimating unknown functions with either varying degrees of smoothness or high interaction orders. Levy process priors have advantages of encouraging sparsity in the expansions and providing automatic selection over the number of basis functions. The unknown regression function is expressed as a weighted sum of tensor product of B-spline basis functions as the elements of an overcomplete system, which can deal with multi-dimensional data. The B-spline basis can express systematically functions with varying degrees of smoothness. By changing a set of degrees of the tensor product basis function, MLABS can adapt the smoothness of target functions due to the nice properties of B-spline bases. The local support of the B-spline basis enables the MLABS to make more delicate predictions than other existing methods in the two-dimensional surface data. Experiments on various simulated and real-world datasets illustrate that the MLABS model has comparable performance on regression and classification problems. We also show that the MLABS model has more stable and accurate predictive abilities than state-of-the-art nonparametric regression models in relatively low-dimensional data.
Convolutional neural network (CNN) is one of the most frequently used deep learning techniques. Various forms of models have been proposed and improved for learning at CNN. When learning with CNN, it is necessary to determine the optimal hyperparameters. However, the number of hyperparameters is so large that it is difficult to do it manually, so much research has been done on automation. A method that uses metaheuristic algorithms is attracting attention in research on hyperparameter optimization. Metaheuristic algorithms are naturally inspired and include evolution strategies, genetic algorithms, antcolony optimization and particle swarm optimization. In particular, particle swarm optimization converges faster than genetic algorithms, and various models have been proposed. In this paper, we propose CNN hyperparameter optimization with linearly decreasing weight particle swarm optimization (LDWPSO). In the experiment, the MNIST data set and CIFAR-10 data set, which are often used as benchmark data sets, are used. By optimizing CNN hyperparameters with LDWPSO, learning the MNIST and CIFAR-10 datasets, we compare the accuracy with a standard CNN based on LeNet-5. As a result, when using the MNIST dataset, the baseline CNN is 94.02% at the 5th epoch, compared to 98.95% for LDWPSO CNN, which improves accuracy. When using the CIFAR-10 dataset, the Baseline CNN is 28.07% at the 10th epoch, compared to 69.37% for the LDWPSO CNN, which greatly improves accuracy.
Adaptive feedback normally provides the greatest accuracy for optical phase measurements. New advances in nitrogen vacancy centre technology have enabled magnetometry via individual spin measurements, which are similar to optical phase measurements but with low visibility. The adaptive measurements that previously worked well with high-visibility optical interferometry break down and give poor results for nitrogen vacancy centre measurements. We use advanced search techniques based on swarm optimisation to design better adaptive measurements that can provide improved measurement accuracy with low-visibility interferometry, with applications in nitrogen vacancy centre magnetometry.
This paper presents an advancement to an approach for model-independent surrogate-based optimization with adaptive batch sampling, known as Adaptive Model Refinement (AMR). While the original AMR method provides unique decisions with regards to when to sample and how many samples to add (to preserve the credibility of the optimization search process), it did not provide specific direction towards where to sample in the design variable space. This paper thus introduces the capability to identify optimum location to add new samples. The location of the infill points is decided by integrating a Gaussian Process-based criteria (q-EI), adopted from Bayesian optimization. The consideration of a penalization term to mitigate interaction among samples (in a batch) is crucial to effective integration of the q-EI criteria into AMR. The new AMR method, called AMR with Penalized Batch Bayesian Sampling (AMR-PBS) is tested on benchmark functions, demonstrating better performance compared to Bayesian EGO. In addition, it is successfully applied to design surface riblets for bio-inspired passive flow control (where high-fidelity samples are given by costly RANS CFD simulations), leading to a 10% drag reduction over the corresponding baseline (i.e., riblet-free aerodynamic surface).
Combinatorial interaction testing is an important software testing technique that has seen lots of recent interest. It can reduce the number of test cases needed by considering interactions between combinations of input parameters. Empirical evidence shows that it effectively detects faults, in particular, for highly configurable software systems. In real-world software testing, the input variables may vary in how strongly they interact, variable strength combinatorial interaction testing (VS-CIT) can exploit this for higher effectiveness. The generation of variable strength test suites is a non-deterministic polynomial-time (NP) hard computational problem cite{BestounKamalFuzzy2017}. Research has shown that stochastic population-based algorithms such as particle swarm optimization (PSO) can be efficient compared to alternatives for VS-CIT problems. Nevertheless, they require detailed control for the exploitation and exploration trade-off to avoid premature convergence (i.e. being trapped in local optima) as well as to enhance the solution diversity. Here, we present a new variant of PSO based on Mamdani fuzzy inference system cite{Camastra2015,TSAKIRIDIS2017257,KHOSRAVANIAN2016280}, to permit adaptive selection of its global and local search operations. We detail the design of this combined algorithm and evaluate it through experiments on multiple synthetic and benchmark problems. We conclude that fuzzy adaptive selection of global and local search operations is, at least, feasible as it performs only second-best to a discrete variant of PSO, called DPSO. Concerning obtaining the best mean test suite size, the fuzzy adaptation even outperforms DPSO occasionally. We discuss the reasons behind this performance and outline relevant areas of future work.
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