Number Of Training Observations Research Articles

Application of Gaussian process regression and asymmetric least squares baseline algorithm on the determination of electrochemical sensor characteristics: A case study on SARS-CoV-2 glucometer

In this study, it was aimed to determine limit of detection, limit of quantification, and signal to noise ratio by the use of SARS-CoV-2 glucometer response data in "Singh, N·K., Ray, P., Carlin, A.F., Morgan, S·C., Magallanes, C., Laurent, L.C., Aronoff-Spencer, E.S., Hall, D.A., 2021b. Dataset on optimization and development of a point-of-care glucometer-based SARS-CoV-2 detection assay using aptamers. Data Brief 38, 107,278.” and by Bayesian optimization and asymmetric least squares baseline algorithm which was used for prediction of response curve and baseline. It was seen that the predicted limit of detection and limit of quantification reached a certain level after a certain number of training observations and ranged between 0.9-16 pM and 2.8–44 pM respectively.

Parallel supervised land-cover classification system for hyperspectral and multispectral images

Hyperspectral and multispectral imagery allows remote-sensing applications such as the land-cover mapping, which is a significant baseline to understand and to monitor the Earth. Furthermore, it is a relevant process for socio-economic activities. For that reason, high land-classification accuracies are imperative, and minor image processing time is essential. In addition, the process of gathering classes’ documented samples is complicated. This implies that the classification system is required to perform with a limited number of training observations. Another point worth mentioning is that there are hardly any methods that can be used analogously for hyperspectral or multispectral images. This paper aims to propose a novel classification system that can be used for both types of images. The designed classification system is composed of a novel parallel feature extraction algorithm, which utilises a cluster of two graphics processing units in combination with a multicore central processing unit (CPU), and an artificial neural network (ANN) particularly devised for the classification of the features ensued by the implemented feature extraction method. To prove the performance of the proposed classification system, it is compared with non-parallel and CPU-only-parallel implementations employing multispectral and hyperspectral databases. Moreover, experiments with different number of samples for training the classifier are performed. Finally, the proposed ANN is compared with a state-of-the-art support vector machine in classification and processing time results.

Comparing the efficiency of digital and conventional soil mapping to predict soil types in a semi-arid region in Iran

The efficiency of different digital and conventional soil mapping approaches to produce categorical maps of soil types is determined by cost, sample size, accuracy and the selected taxonomic level. The efficiency of digital and conventional soil mapping approaches was examined in the semi-arid region of Borujen, central Iran. This research aimed to (i) compare two digital soil mapping approaches including Multinomial logistic regression and random forest, with the conventional soil mapping approach at four soil taxonomic levels (order, suborder, great group and subgroup levels), (ii) validate the predicted soil maps by the same validation data set to determine the best method for producing the soil maps, and (iii) select the best soil taxonomic level by different approaches at three sample sizes (100, 80, and 60 point observations), in two scenarios with and without a geomorphology map as a spatial covariate. In most predicted maps, using both digital soil mapping approaches, the best results were obtained using the combination of terrain attributes and the geomorphology map, although differences between the scenarios with and without the geomorphology map were not significant. Employing the geomorphology map increased map purity and the Kappa index, and led to a decrease in the ‘noisiness’ of soil maps. Multinomial logistic regression had better performance at higher taxonomic levels (order and suborder levels); however, random forest showed better performance at lower taxonomic levels (great group and subgroup levels). Multinomial logistic regression was less sensitive than random forest to a decrease in the number of training observations. The conventional soil mapping method produced a map with larger minimum polygon size because of traditional cartographic criteria used to make the geological map 1:100,000 (on which the conventional soil mapping map was largely based). Likewise, conventional soil mapping map had also a larger average polygon size that resulted in a lower level of detail. Multinomial logistic regression at the order level (map purity of 0.80), random forest at the suborder (map purity of 0.72) and great group level (map purity of 0.60), and conventional soil mapping at the subgroup level (map purity of 0.48) produced the most accurate maps in the study area. The multinomial logistic regression method was identified as the most effective approach based on a combined index of map purity, map information content, and map production cost. The combined index also showed that smaller sample size led to a preference for the order level, while a larger sample size led to a preference for the great group level.

Learning Curves in Classification With Microarray Data

The performance of many repeated tasks improves with experience and practice. This improvement tends to be rapid initially and then decreases. The term "learning curve" is often used to describe the phenomenon. In supervised machine learning, the performance of classification algorithms often increases with the number of observations used to train the algorithm. We use progressively larger samples of observations to train the algorithm and then plot performance against the number of training observations. This yields the familiar negatively accelerating learning curve. To quantify the learning curve, we fit inverse power law models to the progressively sampled data. We fit such learning curves to four large clinical cancer genomic datasets, using three classifiers (diagonal linear discriminant analysis, K-nearest-neighbor with three neighbors, and support vector machines) and four values for the number of top genes included (5, 50, 500, 5,000). The inverse power law models fit the progressively sampled data reasonably well and showed considerable diversity when multiple classifiers are applied to the same data. Some classifiers showed rapid and continued increase in performance as the number of training samples increased, while others showed little if any improvement. Assessing classifier efficiency is particularly important in genomic studies since samples are so expensive to obtain. It is important to employ an algorithm that uses the predictive information efficiently, but with a modest number of training samples (>50), learning curves can be used to assess the predictive efficiency of classification algorithms.

Impossibility of successful classification when useful features are rare and weak

We study a two-class classification problem with a large number of features, out of which many are useless and only a few are useful, but we do not know which ones they are. The number of features is large compared with the number of training observations. Calibrating the model with 4 key parameters--the number of features, the size of the training sample, the fraction, and strength of useful features--we identify a region in parameter space where no trained classifier can reliably separate the two classes on fresh data. The complement of this region--where successful classification is possible--is also briefly discussed.

Hypergraph-Based Anomaly Detection of High-Dimensional Co-Occurrences

This paper addresses the problem of detecting anomalous multivariate co-occurrences using a limited number of unlabeled training observations. A novel method based on using a hypergraph representation of the data is proposed to deal with this very high-dimensional problem. Hypergraphs constitute an important extension of graphs which allow edges to connect more than two vertices simultaneously. A variational Expectation-Maximization algorithm for detecting anomalies directly on the hypergraph domain without any feature selection or dimensionality reduction is presented. The resulting estimate can be used to calculate a measure of anomalousness based on the False Discovery Rate. The algorithm has O(np) computational complexity, where n is the number of training observations and p is the number of potential participants in each co-occurrence event. This efficiency makes the method ideally suited for very high-dimensional settings, and requires no tuning, bandwidth or regularization parameters. The proposed approach is validated on both high-dimensional synthetic data and the Enron email database, where p > 75,000, and it is shown that it can outperform other state-of-the-art methods.

Design of optimal binary filters under joint multiresolution–envelope constraint

This paper examines binary filter design by jointly applying multiresolution design and envelope constraint. In multiresolution design, the value of the designed filter for a configuration is defined at a resolution sufficiently low to have observed the configuration. Preference is given to higher resolutions, but the number of training observations is taken into account. In envelope design, the designed filter is constrained to lie in the envelope between two humanly designed filters. For small samples, the envelope-designed filter has the benefit of being in accord with expert knowledge, whereas for large samples statistical training provides more accurate filter design. To obtain the advantages of both approaches, they can be applied in combination. This can be done in more than a single way. This paper explores joint multiresolution–envelope design, extends the basic propositions for envelope design to the multiresolution setting, considers design consistency, and provides experimental support for the joint approach.

Approximation and estimation bounds for artificial neural networks

For a common class of artificial neural networks, the mean integrated squared error between the estimated network and a target function f is shown to be bounded by O \left ( {{C^2_f}\over n}\right ) + O\left ({nd\over N}{\rm log}\ N\right), where n is the number of nodes, d is the input dimension of the function, N is the number of training observations, and Cf is the first absolute moment of the Fourier magnitude distribution of f. The two contributions to this total risk are the approximation error and the estimation error. Approximation error refers to the distance between the target function and the closest neural network function of a given architecture and estimation error refers to the distance between this ideal network function and an estimated network function. With n ˜ Cf(N/(dlog N))1/2 nodes, the order of the bound on the mean integrated squared error is optimized to be O(Cf((d/N)log N)1/2). The bound demonstrates surprisingly favorable properties of network estimation compared to traditional series and nonparametric curve estimation techniques in the case that d is moderately large. Similar bounds are obtained when the number of nodes n is not preselected as a function of Cf (which is generally not known a priori), but rather the number of nodes is optimized from the observed data by the use of a complexity regularization or minimum description length criterion. The analysis involves Fourier techniques for the approximation error, metric entropy considerations for the estimation error, and a calculation of the index of resolvability of minimum complexity estimation of the family of networks.

Approximation and estimation bounds for artificial neural networks

For a common class of artificial neural networks, the mean integrated squared error between the estimated network and a target functionf is shown to be bounded by $$O\left( {\frac{{\mathop c\nolimits_f^2 }}{n}} \right) + O\left( {\frac{{nd}}{N}\log N} \right)$$ wheren is the number of nodes,d is the input dimension of the function,N is the number of training observations, andC f is the first absolute moment of the Fourier magnitude distribution off. The two contributions to this total risk are the approximation error and the estimation error. Approximation error refers to the distance between the target function and the closest neural network function of a given architecture and estimation error refers to the distance between this ideal network function and an estimated network function. Withn ∼ C f (N/(d logN))1/2 nodes, the order of the bound on the mean integrated squared error is optimized to beO(C f ((d/N) logN)1/2). The bound demonstrates surprisingly favorable properties of network estimation compared to traditional series and nonparametric curve estimation techniques in the case thatd is moderately large. Similar bounds are obtained when the number of nodesn is not preselected as a function ofC f (which is generally not knowna priori), but rather the number of nodes is optimized from the observed data by the use of a complexity regularization or minimum description length criterion. The analysis involves Fourier techniques for the approximation error, metric entropy considerations for the estimation error, and a calculation of the index of resolvability of minimum complexity estimation of the family of networks.