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PubMed2001

Rapid multipoint linkage analysis via inheritance vectors in the Elston-Stewart algorithm.

The calculation of multipoint likelihoods of pedigree data is crucial for extracting the full available information needed for both parametric and nonparametric linkage analysis. Recent mathematical advances in both the Elston-Stewart and Lander-Green algorithms for computing exact multipoint likelihoods of pedigree data have enabled researchers to analyze data sets containing more markers and more individuals both faster and more efficiently. This paper presents novel algorithms that further extend the computational boundary of the Elston-Stewart algorithm. They have been implemented into the software package VITESSE v. 2 and are shown to be several orders of magnitude faster than the original implementation of the Elston-Stewart algorithm in VITESSE v. 1 on a variety of real pedigree data. VITESSE v. 2 was faster by a factor ranging from 168 to over 1,700 on these data sets, thus making a qualitative difference in the analysis. The main algorithm is based on the faster computation of the conditional probability of a component nuclear family within the pedigree by summing over the joint genotypes of the children instead of the parents as done in the VITESSE v. 1. This change in summation allows the parent-child transmission part of the calculation to be not only computed for each parent separately, but also for each locus separately by using inheritance vectors as is done in the Lander-Green algorithm. Computing both of these separately can lead to substantial computational savings. The use of inheritance vectors in the nuclear family calculation represents a partial synthesis of the techniques of the Lander-Green algorithm into the Elston-Stewart algorithm. In addition, the technique of local set recoding is introduced to further reduce the complexity of the nuclear family computation. These new algorithms, however, are not universally faster on all types of pedigree data compared to the method implemented in VITESSE v. 1 of summing over the parents. Therefore, a hybrid algorithm is introduced which combines the strength of both summation methods by using a numerical heuristic to decide which of the two to use for a given nuclear family within the pedigree and is shown to be faster than either method on its own. Finally, this paper discusses various complexity issues regarding both the Elston-Stewart and Lander-Green algorithms and possible future directions of further synthesis.

Algorithms↗
PubMed1981

Impact of prehospital cardiac algorithms on ventricular fibrillation survival rates.

To determine the value of algorithms in the field, a set of cardiac clinical algorithms was developed for and tested by the City of Philadelphia paramedics. A controlled test was carried out by revising the narrative standard operating procedure to reflect algorithm content and giving the algorithms, in pocket-size booklet form, to half the Fire Rescue platoons (43 men). Baseline data included paramedics' characteristics, arrhythmia recognition and management test scores, and data on the number of patients who were discharged alive from the hospital following successful treatment of ventricular fibrillation in the field. Platoons with and without the algorithms served identical areas of the city, did not differ in response times, and were treated similarly with regard to continuing education during the study period. Paramedics who received the algorithms were encouraged, but not required, to use them. Platoons using the algorithms experienced an increase in their ventricular fibrillation patient survival rates from 10.6% to 14.5%; those platoons not using the algorithms had a decrease in patient survival rates from 11.8% to 7.0% (P = 0.0732). There was no statistically significant difference in the paramedics' scores on arrhythmia recognition and management tests given before and after use of the algorithms. Only 39% of the paramedics used the algorithms during actual patient care, but 83% used them as a study guide or for reference between runs. The data suggest that algorithm use may minimize the rate of knowledge and skill decay.

Allied Health Personnel↗
PubMed2004

Interactively optimizing signal-to-noise ratios in expression profiling: project-specific algorithm selection and detection p-value weighting in Affymetrix microarrays.

MOTIVATION: The most commonly utilized microarrays for mRNA profiling (Affymetrix) include 'probe sets' of a series of perfect match and mismatch probes (typically 22 oligonucleotides per probe set). There are an increasing number of reported 'probe set algorithms' that differ in their interpretation of a probe set to derive a single normalized 'signal' representative of expression of each mRNA. These algorithms are known to differ in accuracy and sensitivity, and optimization has been done using a small set of standardized control microarray data. We hypothesized that different mRNA profiling projects have varying sources and degrees of confounding noise, and that these should alter the choice of a specific probe set algorithm. Also, we hypothesized that use of the Microarray Suite (MAS) 5.0 probe set detection p-value as a weighting function would improve the performance of all probe set algorithms. RESULTS: We built an interactive visual analysis software tool (HCE2W) to test and define parameters in Affymetrix analyses that optimize the ratio of signal (desired biological variable) versus noise (confounding uncontrolled variables). Five probe set algorithms were studied with and without statistical weighting of probe sets using the MAS 5.0 probe set detection p-values. The signal-to-noise ratio optimization method was tested in two large novel microarray datasets with different levels of confounding noise, a 105 sample U133A human muscle biopsy dataset (11 groups: mutation-defined, extensive noise), and a 40 sample U74A inbred mouse lung dataset (8 groups: little noise). Performance was measured by the ability of the specific probe set algorithm, with and without detection p-value weighting, to cluster samples into the appropriate biological groups (unsupervised agglomerative clustering with F-measure values). Of the total random sampling analyses, 50% showed a highly statistically significant difference between probe set algorithms by ANOVA [F(4,10) > 14, p < 0.0001], with weighting by MAS 5.0 detection p-value showing significance in the mouse data by ANOVA [F(1,10) > 9, p < 0.013] and paired t-test [t(9) = -3.675, p = 0.005]. Probe set detection p-value weighting had the greatest positive effect on performance of dChip difference model, ProbeProfiler and RMA algorithms. Importantly, probe set algorithms did indeed perform differently depending on the specific project, most probably due to the degree of confounding noise. Our data indicate that significantly improved data analysis of mRNA profile projects can be achieved by optimizing the choice of probe set algorithm with the noise levels intrinsic to a project, with dChip difference model with MAS 5.0 detection p-value continuous weighting showing the best overall performance in both projects. Furthermore, both existing and newly developed probe set algorithms should incorporate a detection p-value weighting to improve performance. AVAILABILITY: The Hierarchical Clustering Explorer 2.0 is available at http://www.cs.umd.edu/hcil/hce/ Murine arrays (40 samples) are publicly available at the PEPR resource (http://microarray.cnmcresearch.org/pgadatatable.asp http://pepr.cnmcresearch.org Chen et al., 2004).

Cluster Analysis↗
PubMed2004

Dual geometric worm algorithm for two-dimensional discrete classical lattice models.

We present a dual geometrical worm algorithm for two-dimensional Ising models. The existence of such dual algorithms was first pointed out by Prokof'ev and Svistunov [Phys. Rev. Lett. 87, 160601 (2001)]]. The algorithm is defined on the dual lattice and is formulated in terms of bond variables and can therefore be generalized to other two-dimensional models that can be formulated in terms of bond variables. We also discuss two related algorithms formulated on the direct lattice, applicable in any dimension. These latter algorithms turn out to be less efficient but of considerable intrinsic interest. We show how such algorithms quite generally can be "directed" by minimizing the probability for the worms to erase themselves. Explicit proofs of detailed balance are given for all the algorithms. In terms of computational efficiency the dual geometrical worm algorithm is comparable to well known cluster algorithms such as the Swendsen-Wang and Wolff algorithms, however, it is quite different in structure and allows for a very simple and efficient implementation. The dual algorithm also allows for a very elegant way of calculating the domain wall free energy.

Journal Article↗
PubMed2006

Clustering algorithm for determining community structure in large networks.

We propose an algorithm to find the community structure in complex networks based on the combination of spectral analysis and modularity optimization. The clustering produced by our algorithm is as accurate as the best algorithms on the literature of modularity optimization; however, the main asset of the algorithm is its efficiency. The best match for our algorithm is Newman's fast algorithm, which is the reference algorithm for clustering in large networks due to its efficiency. When both algorithms are compared, our algorithm outperforms the fast algorithm both in efficiency and accuracy of the clustering, in terms of modularity. Thus, the results suggest that the proposed algorithm is a good choice to analyze the community structure of medium and large networks in the range of tens and hundreds of thousand vertices.

Journal Article↗
PubMed1987

Diagnosing human malformation patterns with a microcomputer: evaluation of two different algorithms.

SYNDROC, a microcomputer-aided differential diagnostic approach to human malformation patterns, is based on a pseudo-Bayesian algorithm. This means that, for each sign, the frequency of this sign in the general population, its frequency in a particular syndrome, and the frequency of that particular syndrome have to be determined. These parameters are easy to find in common syndromes but tend to be difficult for rare or isolated cases. Thus, we implemented a new algorithm called the "descriptive algorithm," which defines a diagnosis by a set of anomalies all having the same weight. To test this algorithm, we analyzed 100 cases representing 100 different syndromes out of the register of the Division of Medical Genetics, Children's Hospital and Medical Center, University of Washington. The descriptive algorithm was allowed to give 3 sets of diagnoses. In 91% of the cases, this algorithm proposed the correct diagnosis (54% in the first window, 28% in the second window, and 9% in the third window). The number of diagnoses proposed was 18.78 +/- 16.57. The same cases were analyzed with the pseudo-Bayesian algorithm. The concordant diagnosis was proposed in 92% of the cases (55% at the top place, 11% at the second place, and 26% at the third place or beyond). The number of diagnoses submitted was 13.5 +/- 11.04. The combined algorithm gave the correct diagnosis in 96% of the cases. This study shows that the descriptive algorithm is as accurate as the pseudo-Bayesian algorithm in diagnosing malformation patterns, but this level is accompanied by an increased number of proposed diagnoses.

Abnormalities, Multiple↗
PubMed2004

Airway resistance by the interrupter technique: which algorithm for measuring pressure?

Airway resistance using the interrupter technique (Rint) can be measured using commercial devices which employ different algorithms for estimating pressure change. We aim to describe differences in Rint due to algorithm. We compared Rint and change in Rint after bronchodilator, using four algorithms to estimate pressure change following interruption: 1) two-point back-extrapolation to interruption from points 70 msec and 30 msec from interruption, and similarly 2) to 15 msec from interruption, 3) at two-thirds from interruption, and 4) near end-interruption. Flow was measured immediately before interruption. Our subjects were 39 asymptomatic children 2-5 years old with previous intermittent wheeze. Rint differed significantly with algorithm. Geometric mean Rint (95% confidence interval (CI)) for algorithms 1-4 were 1.21 kPa x l(-1) x sec (1.18-1.24 kPa x l(-1) x sec), 1.31 kPa x l(-1) x sec (1.28-1.34 kPa x l(-1) x sec), 1.57 kPa x l(-1) x sec (1.54-1.61 kPa x l(-1) x sec) and 1.71 kPa x l(-1) x sec (1.67-1.75 kPa x l(-1) x sec), respectively. Measurement of change in R(int) following bronchodilator (BDR) did not differ on average with algorithm. Geometric means (95% CI) for BDR measurements for algorithms 1-4 were 29.9% (26.0-34.0%), 30.4% (26.4-34.5%), 32.9% (28.8-37.1%), and 31.7% (27.6-35.8%), respectively. However, measurement of change in individuals could differ by up to 40%, depending on algorithm. In conclusion, there are significant differences in Rint, depending on algorithm used to estimate pressure change. Measurement of change in Rint is unaffected on average, although in individuals there could be significant differences. Each laboratory should state its method and use the same algorithm for longitudinal and group data.

Airway Resistance↗
PubMed2001

Latency change estimation for evoked potentials: a comparison of algorithms.

Evoked potentials (EPs) have been widely used to quantify neurological system properties. Changes in EP latency may indicate impending neurological dysfunctions. This paper provides a review and a performance comparison of three classes of latency change estimation algorithms: correlation based, adaptive least mean square (LMS) based, and p-norm based algorithms. Data analysis based on computer simulated data and data from impact acceleration and hypoxia experiments were conducted. This concluded that correlation-based algorithms should only be used when the expected latency change is fixed and the noises are not correlated. While all adaptive LMS type algorithms were capable of tracking and estimating latency changes (fixed or variable) under Gaussian noise conditions, the direct LMS-based algorithm reduced the estimation error power given by traditional filter type LMS algorithms as much as 93%. When periodic interference was present, the frequency selective LMS algorithms outperformed other LMS-based algorithms and reduced of the estimation error power by 89%. Alpha-stable noise processes are better approximations of noises found in various EP analysis applications and adaptive p-norm based algorithms are found to be very robust under such noise conditions, eliminate erroneous abrupt latency changes other algorithms would have produced.

Algorithms↗
PubMed1994

Localization of accessory pathways from the 12-lead electrocardiogram using a new algorithm.

A new algorithm (St. George's algorithm), based on the polarity and morphology of QRS complexes rather than delta waves, was developed for localizing accessory pathways to 1 of 9 sites on the atrioventricular annuli. This was compared with algorithms previously proposed by Skeberis et al (localizing to 1 of 7 sites) and Milstein et al (localizing to 1 of 4 sites). The preexcited 12-lead electrocardiograms recorded during sinus rhythm in 106 consecutive patients (including 60 retrospectively analyzed patients and 46 prospectively analyzed patients) who underwent successful radiofrequency catheter ablation of a single accessory pathway were analyzed by 3 blinded observers using all 3 algorithms. The results were compared with the actual localization of accessory pathways as derived from endocardial mapping during catheter ablation. In all 106 patients, the accuracy of the 3 algorithms for 4 sites on the atrioventricular annuli (as considered by Milstein's method) was 72%, 79%, and 92% for Milstein's, Skeberis', and St. George's algorithms, respectively. For 7 sites (as considered by Skeberis' method), the accuracy was 65% (Skeberis' algorithm) and 88% (St. George's algorithm), and for 9 sites (as considered by our method) the accuracy was 86% (St. George's algorithm). In 46 prospectively analyzed patients, the accuracy of the 3 algorithms for 4 sites was 70% (Milstein's), 67% (Skeberis'), and 87% (St. George's); for 7 sites the accuracy was 61% (Skeberis') and 85% (St. George's), and for 9 sites the accuracy was 85% (St. George's). The reproducibility of St. George's and Skeberis' methods was better than that of Milstein's method.(ABSTRACT TRUNCATED AT 250 WORDS)

Adolescent↗
PubMed2003

Incorporating an improved dose-calculation algorithm in conformal radiotherapy of lung cancer: re-evaluation of dose in normal lung tissue.

BACKGROUND AND PURPOSE: The low density of lung tissue causes a reduced attenuation of photons and an increased range of secondary electrons, which is inaccurately predicted by the algorithms incorporated in some commonly available treatment planning systems (TPSs). This study evaluates the differences in dose in normal lung tissue computed using a simple and a more correct algorithm. We also studied the consequences of these differences on the dose-effect relations for radiation-induced lung injury. MATERIALS AND METHODS: The treatment plans of 68 lung cancer patients initially produced in a TPS using a calculation model that incorporates the equivalent-path length (EPL) inhomogeneity-correction algorithm, were recalculated in a TPS with the convolution-superposition (CS) algorithm. The higher accuracy of the CS algorithm is well-established. Dose distributions in lung were compared using isodoses, dose-volume histograms (DVHs), the mean lung dose (MLD) and the percentage of lung receiving >20 Gy (V20). Published dose-effect relations for local perfusion changes and radiation pneumonitis were re-evaluated. RESULTS: Evaluation of isodoses showed a consistent overestimation of the dose at the lung/tumor boundary by the EPL algorithm of about 10%. This overprediction of dose was also reflected in a consistent shift of the EPL DVHs for the lungs towards higher doses. The MLD, as determined by the EPL and CS algorithm, differed on average by 17+/-4.5% (+/-1SD). For V20, the average difference was 12+/-5.7% (+/-1SD). For both parameters, a strong correlation was found between the EPL and CS algorithms yielding a straightforward conversion procedure. Re-evaluation of the dose-effect relations showed that lung complications occur at a 12-14% lower dose. The values of the TD(50) parameter for local perfusion reduction and radiation pneumonitis changed from 60.5 and 34.1 Gy to 51.1 and 29.2 Gy, respectively. CONCLUSIONS: A simple tissue inhomogeneity-correction algorithm like the EPL overestimates the dose to normal lung tissue. Dosimetric parameters for lung injury (e.g. MLD, V20) computed using both algorithms are strongly correlated making an easy conversion feasible. Dose-effect relations should be refitted when more accurate dose data is available.

Algorithms↗
PubMed2001

The POP learning algorithms: reducing work in identifying fuzzy rules.

A novel fuzzy neural network, the Pseudo Outer-Product based Fuzzy Neural Network (POPFNN), and its two fuzzy-rule-identification algorithms are proposed in this paper. They are the Pseudo Outer-Product (POP) learning and the Lazy Pseudo Outer-Product (LazyPOP) leaning algorithms. These two learning algorithms are used in POPFNN to identify relevant fuzzy rules. In contrast with other rule-learning algorithms, the proposed algorithms have many advantages, such as being fast, reliable, efficient, and easy to understand. POP learning is a simple one-pass learning algorithm. It essentially performs rule-selection. Hence, it suffers from the shortcoming of having to consider all the possible rules. The second algorithm, the LazyPOP learning algorithm, truly identifies the fuzzy rules which are relevant and does not use a rule-selection method whereby irrelevant fuzzy rules are eliminated from an initial rule set. In addition, it is able to adjust the structure of the fuzzy neural network. The proposed LazyPOP learning algorithm is able to delete invalid feature inputs according to the fuzzy rules that have been identified. Extensive experimental results and discussions are presented for a detailed analysis of the proposed algorithms.

Algorithms↗
PubMed2000

A graphic approach to evaluate algorithms of secondary structure prediction.

Algorithms of secondary structure prediction have undergone the developments of nearly 30 years. However, the problem of how to appropriately evaluate and compare algorithms has not yet completely solved. A graphic method to evaluate algorithms of secondary structure prediction has been proposed here. Traditionally, the performance of an algorithm is evaluated by a number, i.e., accuracy of various definitions. Instead of a number, we use a graph to completely evaluate an algorithm, in which the mapping points are distributed in a three-dimensional space. Each point represents the predictive result of the secondary structure of a protein. Because the distribution of mapping points in the 3D space generally contains more information than a number or a set of numbers, it is expected that algorithms may be evaluated and compared by the proposed graphic method more objectively. Based on the point distribution, six evaluation parameters are proposed, which describe the overall performance of the algorithm evaluated. Furthermore, the graphic method is simple and intuitive. As an example of application, two advanced algorithms, i.e., the PHD and NNpredict methods, are evaluated and compared. It is shown that there is still much room for further improvement for both algorithms. It is pointed out that the accuracy for predicting either the alpha-helix or beta-strand in proteins with higher alpha-helix or beta-strand content, respectively, should be greatly improved for both algorithms.

Algorithms↗
PubMed1997

Treatment algorithms in child psychopharmacology research.

Clinical trials in child psychiatry research have increased in complexity. Several factors have contributed to this change, including the need to compare multiple therapies, to re-create clinically relevant situations in research, to standardize treatment approaches, to account for the impact of comorbidity, to respond to the needs of individual patients, and to optimize treatment accordingly. To preserve the clinical and internal validity of the experimental interventions vis-à-vis their increasing complexity, researchers have started developing treatment algorithms. These deductive systems for handling data allow us to standardize and incorporate clinical judgment into study designs through the adoption of a stepwise decision making process. Treatment algorithms are different from treatment guidelines. Guidelines are general recommendations that apply to groups of patients with certain characteristics; they are not fully detailed and are created with the expectation that clinical judgment will be applied in individual cases. Algorithms are patient specific, are intended to capture all the relevant details of the clinical situation, and require minimal clinical judgment for their clinical application; they are designed to minimize the role of clinical judgment in research protocols. The entire multistep algorithm is tested in a clinical trial, not the single steps that constitute the algorithm, so proving the efficacy of an algorithm cannot replace a controlled assessment of the individual treatments embedded in the algorithm. Some characteristics, properties, and limitations of algorithms in child psychiatry and psychopharmacology research are presented along with two examples of algorithms currently used in child and adolescent psychopharmacology. Although treatment algorithms seldom have been used in pediatric psychiatry and psychopharmacology, there are indications that their use will increase in the near future and will allow the standardized introduction of clinical judgment into research design.

Adolescent↗
PubMed1996

PARODS--a study of parallel algorithms for ordering DNA sequences.

A suite of parallel algorithms for ordering DNA sequences (termed PARODS) is presented. The algorithms in PARODS are based on an earlier serial algorithm, ODS, which is a physical mapping algorithm based on simulated annealing. Parallel algorithms for simulated annealing based on Markov chain decomposition are proposed and applied to the problem of physical mapping. Perturbation methods and problem-specific annealing heuristics are proposed and described. Implementations of parallel Single Instruction Multiple Data (SIMD) algorithms on a 2048 processor MasPar MP-2 system and implementations of parallel Multiple Instruction Multiple Data (MIMD) algorithms on an 8 processor Intel iPSC/860 system are presented. The convergence, speedup and scalability characteristics of the aforementioned algorithms are analyzed and discussed. The best SIMD algorithm is shown to have a speedup of approximately 1000 on the 2048 processor MasPar MP-2 system, whereas the best MIMD algorithm is shown to have a speedup of approximately 5 on the 8 processor Intel iPSC/860 system.

Algorithms↗
PubMed2006

Comparison of atrial signal extraction algorithms in 12-lead ECGs with atrial fibrillation.

Analysis of atrial rhythm is important in the treatment and management of patients with atrial fibrillation. Several algorithms exist for extracting the atrial signal from the electrocardiogram (ECG) in atrial fibrillation, but there are few reports on how well these techniques are able to recover the atrial signal. We assessed and compared three algorithms for extracting the atrial signal from the 12-lead ECG. The 12-lead ECGs of 30 patients in atrial fibrillation were analyzed. Atrial activity was extracted by three algorithms, Spatiotemporal QRST cancellation (STC), principal component analysis (PCA), and independent component analysis (ICA). The amplitude and frequency characteristics of the extracted atrial signals were compared between algorithms and against reference data. Mean (standard deviation) amplitude of QRST segments of V1 was 0.99 (0.54) mV, compared to 0.18 (0.11) mV (STC), 0.19 (0.13) mV (PCA), and 0.29 (0.22) mV (ICA). Hence, for all algorithms there were significant reductions in the amplitude of the ventricular activity compared with that in V1. Reference atrial signal amplitude in V1 was 0.18 (0.11) mV, compared to 0.17 (0.10) mV (STC), 0.12 (0.09) mV (PCA), and 0.18 (0.13) mV (ICA) in the extracted atrial signals. PCA tended to attenuate the atrial signal in these segments. There were no significant differences for any of the algorithms when comparing the amplitude of the reference atrial signal with that of the extracted atrial signals in segments in which ventricular activity had been removed. There were no significant differences between algorithms in the frequency characteristics of the extracted atrial signals. There were discrepancies in amplitude and frequency characteristics of the atrial signal in only a few cases resulting from notable residual ventricular activity for PCA and ICA algorithms. In conclusion, the extracted atrial signals from these algorithms exhibit very similar amplitude and frequency characteristics. Users of these algorithms should be observant of residual ventricular activities which can affect the analysis of the fibrillatory waveform in clinical practice.

Algorithms↗
PubMed2004

An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision.

After [15], [31], [19], [8], [25], [5], minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper is to provide an experimental comparison of the efficiency of min-cut/max flow algorithms for applications in vision. We compare the running times of several standard algorithms, as well as a new algorithm that we have recently developed. The algorithms we study include both Goldberg-Tarjan style "push-relabel" methods and algorithms based on Ford-Fulkerson style "augmenting paths." We benchmark these algorithms on a number of typical graphs in the contexts of image restoration, stereo, and segmentation. In many cases, our new algorithm works several times faster than any of the other methods, making near real-time performance possible. An implementation of our max-flow/min-cut algorithm is available upon request for research purposes.

Algorithms↗
PubMed2005

Genetic-based EM algorithm for learning Gaussian mixture models.

We propose a genetic-based expectation-maximization (GA-EM) algorithm for learning Gaussian mixture models from multivariate data. This algorithm is capable of selecting the number of components of the model using the minimum description length (MDL) criterion. Our approach benefits from the properties of Genetic algorithms (GA) and the EM algorithm by combination of both into a single procedure. The population-based stochastic search of the GA explores the search space more thoroughly than the EM method. Therefore, our algorithm enables escaping from local optimal solutions since the algorithm becomes less sensitive to its initialization. The GA-EM algorithm is elitist which maintains the monotonic convergence property of the EM algorithm. The experiments on simulated and real data show that the GA-EM outperforms the EM method since: 1) We have obtained a better MDL score while using exactly the same termination condition for both algorithms. 2) Our approach identifies the number of components which were used to generate the underlying data more often than the EM algorithm.

Algorithms↗
PubMed2006

Ordering and finding the best of K > 2 supervised learning algorithms.

Given a data set and a number of supervised learning algorithms, we would like to find the algorithm with the smallest expected error. Existing pairwise tests allow a comparison of two algorithms only; range tests and ANOVA check whether multiple algorithms have the same expected error and cannot be used for finding the smallest. We propose a methodology, the MultiTest algorithm, whereby we order supervised learning algorithms taking into account 1) the result of pairwise statistical tests on expected error (what the data tells us), and 2) our prior preferences, e.g., due to complexity. We define the problem in graph-theoretic terms and propose an algorithm to find the "best" learning algorithm in terms of these two criteria, or in the more general case, order learning algorithms in terms of their "goodness." Simulation results using five classification algorithms on 30 data sets indicate the utility of the method. Our proposed method can be generalized to regression and other loss functions by using a suitable pairwise test.

Algorithms↗