# From margins to probabilities in multiclass learning problems

Our purpose is to estimate conditional probabilities of output labels in multiclass classification problems. Adaboost provides highly accurate classifiers and has potential to estimate conditional probabilities. However, the conditional probability estimated by Adaboost tends to overfit to training samples.

We propose loss functions for boosting that provide shrinkage estimator. The effect of regularization is realized by shrinkage of probabilities toward the uniform distribution. Numerical experiments indicate that boosting algorithms based on proposed loss functions show significantly better results than existing boosting algorithms for estimation of conditional probabilities.

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Authors Authors and affiliations Takafumi Kanamori. Conference paper.

### An incremental learning vector quantization algorithm for pattern classification

This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Freund, Y. Friedman, J. Dietterich, T. Schapire, R. In: Proc.

Bartlett, P. Zhang, T. Cortes, C. Vapnik, V. Gruber, M.We study the problem of multiclass classification within the framework of error correcting output codes ECOC using margin-based binary classifiers.

An important open problem in this context is how to measure the distance between class codewords and the outputs of the classifiers. In this paper we propose a new decoding function that combines the margins through an estimate of their class conditional probabilities.

**Multi class Support Vector Machine (SVM) based classification - own data program**

We report experiments using support vector machines as the base binary classifiers, showing the advantage of the proposed decoding function over other functions of the margin commonly used in practice. We also present new theoretical results bounding the leave-one-out error of ECOC of kernel machines, which can be used to tune kernel parameters. An empirical validation indicates that the bound leads to good estimates of kernel parameters and the corresponding classifiers attain high accuracy.

Documents: Advanced Search Include Citations. Authors: Advanced Search Include Citations. Venue: Proceedings of the 15th annual conference on arti intelligence Citations: 4 - 3 self. Abstract Abstract.

Keyphrases multiclass learning problem kernel parameter corresponding classifier new theoretical result support vector machine good estimate important open problem empirical validation margin-based binary classifier class codewords multiclass classification leave-one-out error base binary classifier decoding function high accuracy class conditional probability output code kernel machine new decoding function.

Powered by:.We study the problem of multiclass classification within the framework of error correcting output codes ECOC using margin-based binary classifiers. An important open problem in this context is how to measure the distance between class codewords and the outputs of the classifiers.

In this paper we propose a new decoding function that combines the margins through an estimate of their class conditional probabilities. We report experiments using support vector machines as the base binary classifiers, showing the advantage of the proposed decoding function over other functions of the margin commonly used in practice.

We also present new theoretical results bounding the leave-one-out error of ECOC of kernel machines, which can be used to tune kernel parameters. An empirical validation indicates that the bound leads to good estimates of kernel parameters and the corresponding classifiers attain high accuracy.

Documents: Advanced Search Include Citations. Authors: Advanced Search Include Citations. Venue: In F. Abstract Abstract. Keyphrases multiclass learning problem kernel parameter corresponding classifier new theoretical result support vector machine good estimate important open problem empirical validation margin-based binary classifier class codewords multiclass classification leave-one-out error base binary classifier decoding function high accuracy class conditional probability output code kernel machine new decoding function.

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## Multiclass Boosting Algorithms for Shrinkage Estimators of Class Probability

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Latest commit. Git stats 1, commits. Failed to load latest commit information. Aug 1, Prototype classifiers have been studied for many years. However, few methods can realize incremental learning. On the other hand, most prototype classifiers need users to predetermine the number of prototypes; an improper prototype number might undermine the classification performance. To deal with these issues, in the paper we propose an online supervised algorithm named Incremental Learning Vector Quantization ILVQ for classification tasks.

The proposed method has three contributions. Therefore, unlike most current prototype classifiers, ILVQ needs no prior knowledge of the number of prototypes or their initial value. Results of experiments show that the proposed ILVQ can accommodate the incremental data environment and provide good recognition performance and storage efficiency.

Prototype based method [ 11 ] is a class of powerful tools in classification family. It searches for a set of representative prototypes that reflects the distribution in original data space.

Then the label of a test sample, usually called query, is defined by the previously generated set of prototypes [ 6 ] shows that the error rate of prototype based classifiers is at most twice of Bayes error rate. Therefore, Prototype based method has been widely used in object classification [ 31 ], visualization recognition system [ 3230 ], optimization [ 12 ], and subspace learning [ 26 ].

It applies all samples in training set as prototypes. NNC works well on large training set. But a trivial consequence of NNC is the large size of prototype sets that aggravates the computation burden. According to this, some different ways [ 710131820232528 ] of learning prototypes have been proposed recently. But all these typical prototype classifiers have some shortcomings.

The learning effect will be very poor when it is used for incremental applications. Under many circumstances, we are not able to avail the prior knowledge about the distributions of data from each class. Therefore, the learning performances will be affected by improper initial values.

## From margins to probabilities in multiclass learning problems

More importantly, online learning can not be achieved because many people often initialize them with partial training samples.To browse Academia. Skip to main content. Log In Sign Up. Download Free PDF. From margins to probabilities in multiclass learning problems ECAI, Massimiliano Pontil. Download PDF. A short summary of this paper.

### Multiclass Boosting Algorithms for Shrinkage Estimators of Class Probability

From margins to probabilities in multiclass learning problems. We study the problem of multiclass classification within be extended to the latter one. In the second step a new input is the framework of error correcting output codes ECOC using classified by computing the vector formed by the outputs of the clas- margin-based binary classifiers.

An important open problem in this sifiers, and choosing the class whose context is how to measure the distance between class codewords and the outputs of the classifiers. In this paper we propose a new decod- corresponding row is closest to. We also present new theoretical re- sults bounding the leave-one-out error of ECOC of kernel machines, where is the decoding function. However, many real world learning problems re- quire that inputs are mapped into one of several possible categories.

The extension of a binary algorithm to its multiclass counterpart where is a loss function. An alternative consists weighting the confidence of each classifier thus allowing a more ro- in reducing a multiclass problem into several binary sub-problems. The simplest loss function one can use Perhaps the most general reduction scheme is the information the- is the linear loss for which but several other oretic method based on error correcting output codes ECOCin- choices are possible and it is not clear which one should work the F troduced by Dietterich and Bakiri [5] and more recently extended best.

ECOC work in two steps: training and classification. Dur- ing the first step, binary classifiers are trained on dichotomies learning algorithm Allwein, Shapire and Singer [1] proposed to set to be the same loss function used by that algorithm.

First, the use of conditional dichotomies. Second, the decoding function is itself a class con- classifier. Whenpoints in class are not used to train ditional probability which can give an estimate of multiclassification the th classifier. Thus each class is encoded by the th row confidence. This approach is discussed in Section 2. In Section 3 of matrix which we also denoted by.

Typically the classi- we present experiments, using SVM as the underlying binary clas- fiers are trained independently. This approach is known as multi-call sifiers, which enlighten the advantage over other proposed decoding approach.

Recent works [8, 2] considered also the case where classi- schemes. In this paper We present a general bound on the leave one out error in the case we focus on the former approach although some of the results may of ECOC of kernel machines.

The bound can be used for estimat- ing optimal kernel parameters. We report experiments showing Dept. Characteristics of the Datasets used We have seen that a loss function of the margin presents some advan- tage over the standard Hamming distance because it can encode the Name Classes Train Test Inputs confidence of each classifier in the ECOC.

This confidence is, how- Anneal 5 - 38 ever, a relative quantity, i. Thus, just using a linear loss function Glass 6 - 9 may introduce some bias in the final classification in the sense that Letter 26 16 classifiers with a larger output range will receive a higher weight. A straightforward normalization in Soybean 19 - 35 some interval, e.

We can now assume a simple model for the prob- ability of given the codebits.Multiclass classification. Threshold optimization. Settings: Features handling. Settings: Feature generation. Settings: Feature reduction. Settings: Hyperparameters optimization. Setting: Weighting strategy. Setting: Probability calibration.

Two-class classification is used when the target can be one of two categories e. Multi-class classification is used when targets can be one of many categories e. DSS can build predictive models for each of these kinds of learning tasks. Available options, algorithms and result screens will vary depending on the kind of learning task. DSS cannot handle large number of classes.

We recommend that you do not try to use machine learning with more than about 50 classes. You must ensure that all classes are detected while creating the machine learning task. Make sure that this sample includes at least one row for each possible class. If some classes are not detected on this sample but found when fitting the algorithm, training will fail. Furthermore, you need to ensure that all classes are present both in the train and the test set.

You might need to adjust the split settings for that assertion to hold true. Note that these constraints are more complex to handle with large number of classes and very rare classes. Enabling this setting allows you to train partitioned prediction models on partitioned datasets. When training with this setting, DSS creates one sub model or model partition per partition of your dataset.

For more information, see Partitioned Models. Once the model is trained, DSS evaluates its performance on the test set. By default, DSS randomly splits the input dataset into a training and a test set. The fraction of data used for training can be specified in DSS. Furthermore, depending on the engine DSS can perform this split, random or sorted, from a subsample of the dataset.

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