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classifier confidence

python - how to get a classifier's confidence score for a prediction in sklearn? - stack overflow

python - how to get a classifier's confidence score for a prediction in sklearn? - stack overflow

I suspect that I would use the score() function, but I seem to keep implementing it correctly. I don't know if that's the right function or not, but how would one get the confidence percentage of a classifier's prediction?

For those estimators which do not implement predict_proba() method, you can construct confidence interval by yourself using bootstrap concept (repeatedly calculate your point estimates in many sub-samples).

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how to get [sgie] classifier confidence in python - deepstream sdk - nvidia developer forums

how to get [sgie] classifier confidence in python - deepstream sdk - nvidia developer forums

Hi, I was trying to get result of classifier from classifier-meta using classifier_meta.confidence but not getting success can any one suggest how to get classify object confidence (like object_meta.confidence)

The sample just have one primary infer element, if you want to get objects confidence value from secondary infer element, you need to do some customization. you can refer to test2 sample for how to add secondary infer elements.

multiple classifier system using classification confidence for texture classification | springerlink

multiple classifier system using classification confidence for texture classification | springerlink

This paper proposes a simple yet effective novel classifier fusion strategy for multi-class texture classification. The resulting classification framework is named as Classification Confidence-based Multiple Classifier Approach (CCMCA). The proposed training based scheme fuses the decisions of two base classifiers (those constitute the classifier ensemble) using their classification confidence to enhance the final classification accuracy. 4-fold cross validation approach is followed to perform experiments on four different texture databases those vary in terms of orientation, number of texture classes and complexity. Apart from its simplicity, the proposed CCMCA method shows better and consistent performance with lowest standard deviation as compared to fixed rule and simple trainable fusion techniques irrespective of the feature set used across all the databases used in the experiment. The performance gain of the proposed CCMCA method over other competing methods is found to be statistically significant.

Dash JK, Mukhopadhyay S, Prabhakar N, Garg M, Khandelwal N (2013) Content-based image retrieval for interstitial lung diseases using classification confidence. In: SPIE Medical Imaging, pp. 86,702Y86,702Y. International Society for Optics and Photonics

Farrell KR, Ramachandran RP, Sharma M, Mammone RJ (1997) Sub-word speaker verification using data fusion methods. In: Neural Networks for Signal Processing [1997] VII. Proceedings of the 1997 IEEE Workshop. IEEE, pp 531540

Huang Y, Suen C (1993) The behavior-knowledge space method for combination of multiple classifiers. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Institute of Electrical Engineers Inc (IEEE), pp 347347

Ma L, Liu X, Song L, Liu Y, Zhou C, Zhao X, Zhao Y (2014) A new classifier fusion method based on confusion matrix and classification confidence for recognizing common ct imaging signs of lung diseases. In: SPIE Medical Imaging, pp. 90,351H90,351H. International Society for Optics and Photonics

Ojala T, Maenpaa T, Pietikainen M, Viertola J, Kyllonen J, Huovinen S (2002) Outex-new framework for empirical evaluation of texture analysis algorithms. In: Proceedings 16th International Conference on Pattern Recognition, 2002, vol 1. IEEE, pp 701706

Ojala T, Menp T, Viertola J, Kyllnen J, Pietikinen M (2002) Empirical evaluation of mpeg-7 texture descriptors with a large-scale experiment. In: Proceedings 2nd International Workshop on Texture Analysis and Synthesis, Copenhagen, Denmark, pp 99102

Roli F, Kittler J, Fumera G, Muntoni D (2002) An experimental comparison of classifier fusion rules for multimodal personal identity verification systems. In: Multiple Classifier Systems. Springer, pp 325335

This work has been supported by Ministry of Communications and Information Technology, Department of Electronics and Information Technology, Govt. of India, Grant number 1(3)2009-ME&TMD and 1(2)2013-ME&TMD/ESDA. Thanks to Indian Institute of Technology Kharagpur for funding our research. Authors are thankful to National Institute of Science and Technology, Berhmapur, Odisha, India 761008 for extending its research facility.

Dash, J.K., Mukhopadhyay, S. & Gupta, R.D. Multiple classifier system using classification confidence for texture classification. Multimed Tools Appl 76, 25352556 (2017). https://doi.org/10.1007/s11042-015-3231-z

confidence intervals for machine learning

confidence intervals for machine learning

Confidence intervals are a way of quantifying the uncertainty of an estimate. They can be used to add a bounds or likelihood on a population parameter, such as a mean, estimated from a sample of independent observations from the population. Confidence intervals come from the field of estimation statistics.

A confidence interval to contain an unknown characteristic of the population or process. The quantity of interest might be a population property or parameter, such as the mean or standard deviation of the population or process.

A confidence interval is different from a tolerance interval that describes the bounds of data sampled from the distribution. It is also different from a prediction interval that describes the bounds on a single observation. Instead, the confidence interval provides bounds on a population parameter, such as a mean, standard deviation, or similar.

The value of a confidence interval is its ability to quantify the uncertainty of the estimate. It provides both a lower and upper bound and a likelihood. Taken as a radius measure alone, the confidence interval is often referred to as the margin of error and may be used to graphically depict the uncertainty of an estimate on graphs through the use of error bars.

We can also say that the CI tells us how precise our estimate is likely to be, and the margin of error is our measure of precision. A short CI means a small margin of error and that we have a relatively precise estimate [] A long CI means a large margin of error and that we have a low precision

Confidence intervals belong to a field of statistics called estimation statistics that can be used to present and interpret experimental results instead of, or in addition to, statistical significance tests.

Estimation gives a more informative way to analyze and interpret results. [] Knowing and thinking about the magnitude and precision of an effect is more useful to quantitative science than contemplating the probability of observing data of at least that extremity, assuming absolutely no effect.

These estimates of uncertainty help in two ways. First, the intervals give the consumers of the model an understanding about how good or bad the model may be. [] In this way, the confidence interval helps gauge the weight of evidence available when comparing models. The second benefit of the confidence intervals is to facilitate trade-offs between models. If the confidence intervals for two models significantly overlap, this is an indication of (statistical) equivalence between the two and might provide a reason to favor the less complex or more interpretable model.

It is common to use classification accuracy or classification error (the inverse of accuracy) to describe the skill of a classification predictive model. For example, a model that makes correct predictions of the class outcome variable 75% of the time has a classification accuracy of 75%, calculated as:

Classification accuracy or classification error is a proportion or a ratio. It describes the proportion of correct or incorrect predictions made by the model. Each prediction is a binary decision that could be correct or incorrect. Technically, this is called a Bernoulli trial, named for Jacob Bernoulli. The proportions in a Bernoulli trial have a specific distribution called a binomial distribution. Thankfully, with large sample sizes (e.g. more than 30), we can approximate the distribution with a Gaussian.

In statistics, a succession of independent events that either succeed or fail is called a Bernoulli process. [] For large N, the distribution of this random variable approaches the normal distribution.

Where interval is the radius of the confidence interval, error and accuracy are classification error and classification accuracy respectively, n is the size of the sample, sqrt is the square root function, and z is the number of standard deviations from the Gaussian distribution. Technically, this is called the Binomial proportion confidence interval.

In fact, if we repeated this experiment over and over, each time drawing a new sample S, containing [] new examples, we would find that for approximately 95% of these experiments, the calculated interval would contain the true error. For this reason, we call this interval the 95% confidence interval estimate

By default, it makes the Gaussian assumption for the Binomial distribution, although other more sophisticated variations on the calculation are supported. The function takes the count of successes (or failures), the total number of trials, and the significance level as arguments and returns the lower and upper bound of the confidence interval.

The example below demonstrates this function in a hypothetical case where a model made 88 correct predictions out of a dataset with 100 instances and we are interested in the 95% confidence interval (provided to the function as a significance of 0.05).

The assumptions that underlie parametric confidence intervals are often violated. The predicted variable sometimes isnt normally distributed, and even when it is, the variance of the normal distribution might not be equal at all levels of the predictor variable.

The bootstrap is a simulated Monte Carlo method where samples are drawn from a fixed finite dataset with replacement and a parameter is estimated on each sample. This procedure leads to a robust estimate of the true population parameter via sampling.

The procedure can be used to estimate the skill of a predictive model by fitting the model on each sample and evaluating the skill of the model on those samples not included in the sample. The mean or median skill of the model can then be presented as an estimate of the model skill when evaluated on unseen data.

Recall that a percentile is an observation value drawn from the sorted sample where a percentage of the observations in the sample fall. For example, the 70th percentile of a sample indicates that 70% of the samples fall below that value. The 50th percentile is the median or middle of the distribution.

First, we must choose a significance level for the confidence level, such as 95%, represented as 5.0% (e.g. 100 95). Because the confidence interval is symmetric around the median, we must choose observations at the 2.5th percentile and the 97.5th percentiles to give the full range.

We will perform the bootstrap procedure 100 times and draw samples of 1,000 observations from the dataset with replacement. We will estimate the mean of the population as the statistic we will calculate on the bootstrap samples. This could just as easily be a model evaluation.

I think, the sentence There is a 95% likelihood that the range 0.741 to 0.757 covers the true statistic median. should be There is a 95% likelihood that the range 0.741 to 0.757 covers the true statistic MEAN. because, what you do in code is: # calculate and store statistic statistic = mean(sample)

In general statistical problems, usually we reject a CI that includes or crosses the null (0, or 1), but here our CI can only represent 0-1, so it could include one of these values and still have a significant p value. Is that correct?

I have a question regarding the application of bootstrapping for predictions. After fitting a machine learning model on training data, we use the trained model to predict the test data. Can i apply bootstrapping method on our predictions directly, to get confidence intervals, without splitting each bootstrap sample to train and test and fitting a model to each bootstrap sample?

How do you think youd go about this? Lets say you went through the usual ML steps get data, featurize, train, cross validate, test. Now you have a final model in hand, but you want to give a quantitative way of how tight those metrics (precision/recall/accuracy) are.

It sounds like training multiple models using boostrap resampled training samples and get metrics on the test set for all models? Would it be meaningful to combine the metrics from multiple models as a representative of the final model in hand? Also, could something similar to the concept of alpha be used to make bounds around these?

Thanks for the great post Jason, I have some travel data with information about start / end times. If I build a predictive model, I would like to make a route prediction with a confidence interval . say my features were miles_to_drive, and road_type (highway , local, etc, etc) and my target was drive_time. In this scenario how would you draw from your sample data set to make a prediction with confidence interval? Since confidence interval is a population statistic, could I restrict the set of samples of my dataset based on a filter that is close to the input set of features, or is that a violation of CI?

Hello Jason, I see the binomial distribution can be used to compute confidence intervals on a test set. But, what should we do when doing k-fold crossvalidation? In that case, we have k test partition and k confidence intervals could be computed. But, do you know if it is possible to combine all confidence intervals into one? or obtain a single confidence interval from the crossvalidation procedure?

I prefer to pick a model and then re-evaluate with use a boostrap estimate of model performance: https://machinelearningmastery.com/calculate-bootstrap-confidence-intervals-machine-learning-results-python/

For accuracy as an interval, I suppose one would perform a CV routine, where n represents the fold of the CV and not the nr of examples in the dataset: if the cv fold n > 30, then you may use the parametric method if the cv fold n <30, you should use the non parametric method

Checking normality in the estimates/predictions distribution, and applying well known Gaussian alike methods to find those intervals Applying non-parametric methodologies like bootstraping, so we do not need to assume/check/care whether our distribution is normal

Hi Jason, I have created the sequence labeling model and found the F1 score on validation data nut now, Suppose we have a file to predict the tag i.e sequence labeling such as:- Machine learning articles can be found on machinelearning.

I have printed out the score mean sample list (see scores list) with the lower (2.5%) and upper (97.5%) percentile/border to represent the 95% confidence intervals meaning that there is a 95% likelihood that the range 0.741 to 0.757 covers the true statistic mean.

Ive been reading about confidence intervals lately and Im having a difficult time reconciling the sample definitions provided here with some other resources out there and I wanted to get your opinion on it. In this post and in your statistics book which I have been reading, you give the example Given the sample, there is a 95% likelihood that the range x to y covers the true model accuracy. This definition seems simple enough and other sites out there corroborate this definition. However, some other resources seem to indicate this might not be correct. For example, https://stattrek.com/estimation/confidence-interval.aspx says:

Some people think this means there is a 90% chance that the population mean falls between 100 and 200. This is incorrect. Like any population parameter, the population mean is a constant, not a random variable. It does not change. The probability that a constant falls within any given range is always 0.00 or 1.00 A 90% confidence level means that we would expect 90% of the interval estimates to include the population parameter

The semantics of this definition are a bit confusing to me, especially since word choice and ordering in statistics seem to require more precision than in other fields to be correct. So to be specific, what Im trying to understand is the difference here:

These appear to be different in that the former definition seems to specifically refer to the probability of the sample in question containing the parameter, and the latter definition is talking about multiple experiments.

In sentence: interval = z * sqrt( (accuracy * (1 accuracy)) / n) This works only for a sinlge run on train/test or can I run multiples times, e.g., repeat and average results to use the same formula?

When training and testing a machine learning model, if I split the dataset just once, I may end up with the good portion so I can have a good performance. I may also end up with the bad portion so I can have a poor performance.

But a colleague of mine, whos from a statistics background, told me that cross validation was not needed. Instead, split the data once, train and test the model, then simply use the confidence interval to estimate the performance. For example, I split my data just once, run the model, my AUC ROC is 0.80 and my 95% confidence interval is 0.05. Then the range of AUC ROC is .80+-0.05, which ends up with 0.75 to 0.85. Now I know the range of my models performance without doing cross validation.

I have a question regarding the bootstrap method. At first, we have assumed that the classification error (or accuracy) is normally distributed around the true value. For the bootstrap method, we need some samples from a dataset. In the classification case, this means to me that we need several classification errors (from several datasets) to estimate the distribution of the classification error. Is that correct?

Thanks for the post. I have a question about applying the bootstrap resampling method to get confidence interval for classification metrics like precision and recall. In my practice, I find that the bootstrapped confidence interval does not capture the point estimate and I dont know why. My approach is basically: 1. Split train and val set 2. Repeat for N bootstrap rounds { a. Sample with replacement and get train* and val* b. Fit classifier on train* c. calculate classification metrics (precision and recall at a threshold) on val* } 3. Get the confidence interval based on these bootstrapped metrics. However the confidence interval often does not cover the point estimate, i.e. the precision and recall estimated on the original (unsampled) train and val set. In fact, if I plot the precision-recall curve for each bootstrap rounds, these curves tend to have a different shape from the one calculated using the original train and val set.

I know bootstrapping has some bias, i.e. a classfier trained on the original (unsampled) train set is essentially different from the one trained on bootstrapped train* set. Does it mean that I should only use bootstrapping to calculate the variance, and not the confidence interval for precision / recall?

how to report classifier performance with confidence intervals

how to report classifier performance with confidence intervals

After the final model has been prepared on the training data, it can be used to make predictions on the validation dataset. These predictions are used to calculate a classification accuracy or classification error.

Where error is the classification error, const is a constant value that defines the chosen probability, sqrt is the square root function, and n is the number of observations (rows) used to evaluate the model. Technically, this is called the Wilson score interval.

This is based on some statistics of sampling theory that takes calculating the error of a classifier as a binomial distribution, that we have sufficient observations to approximate a normal distribution for the binomial distribution, and that via the central limit theorem that the more observations we classify, the closer we will get to the true, but unknown, model skill.

Often standard deviation of CV score is used to capture model skill variance, perhaps that is generally sufficient and we can leave confidence intervals for presenting the final model or specific predictions?

Ah @Simone, by the way, if n is equal to the number of all observations that is a type of cross-validation that is called LOOCV (Leave-one-out cross-validation) and uses a single observation from the original sample as the validation data, and the remaining observations as the training data.

Mach Learn. 2018; 107(12): 18951922. Published online 2018 May 9. doi: 10.1007/s10994-018-5714-4. PMCID: PMC6191021, PMID: 30393425. Bootstrapping the out-of-sample predictions for efficient and accurate cross-validation. Ioannis Tsamardinos, lissavet Greasidou (corresponding author), and Giorgos Borboudakis.

Well @Simone, from the point of view of a developer if you take a look at the scikit-learn documentation and go over the section 3.1.1. Computing cross-validated metrics (https://scikit-learn.org/stable/modules/cross_validation.html#computing-cross-validated-metrics) you will see that the 95% confidence interval of the score estimate is reported as Jason states in this post.

This leads to the fundamental problem that accuracy or classification error itself is often mediocre to useless metric because data sets usually are imbalanced. And hence the confidence on that error is just as useless.

I found this post for a different reason as I wanted to find if anyone else does what i do, namely provide metrics grouped by class probability. What is the precision if the model has 0.9 class probability vs 0.6 for example. That can be very useful information for end users because the metric will often vary greatly based on class probability.

Thomas, I think Ive done what you described. I wrote a function to calculate a hand full of different performance metrics at different probability cutoffs and had it stored in a data frame. This helped me choose a probability cutoff that balanced the needs of the business. I can share the code of its what your looking for.

The classifier is assigning labels as expected. The problem I am facing is that the classifier is also assigning labels or group customer code to the customers although the customer name does not match closely with the training data. It is doing the best possible match. It is problem for me because I need to manually ungroup these customers. Can you suggest how to overcome this problem? Is it possible to know classifier correct probability for each predicted label? If yes, then I can ignore the once with low probability.

Hi Jason, I am not sure if anyone else brought this up but Ive found one issue here. The confidence interval based measure you suggested is not the Wilson score interval. according to the Wikipedia page(which is cited in that link). Its actually Normal approximation interval which is above Wilson score paragraph. Correct me if I am wrong.

With 150 examples I decide to use a 100 repeated 5-fold Cross Validation to understand the behavior of my classifier. At this point I have 1005 results and I can use the mean and std dev of the error rates to estimate the variance of the model skills:

What are the options one has for reporting on final model skill with a range for uncertainty in each case? Should one have still held out a number of datapoints for validation+binomial confidence interval? Is it too late to use the bootstrap confidence intervals as the final model was trained?

Thanks Jason. I found your other post https://machinelearningmastery.com/difference-test-validation-datasets/ very helpful. Can I confirm that the above procedure of reporting classifier performance with confidence intervals is relevant for the final trained model? If that is so, it seems that the validation dataset mentioned should be called test set to align with the definitions of the linked post?

I am running a classifier with a training set of 41 and a validation set of 14 (55 total observations). I rerun this 50 times with different random slices of the data as training and test. Obviously I cannot make confidence intervals with this small validation set.

Thank you for the quick reply and apologies for my late response. I am dealing with social science data and the validation set is rather limited. I am worried about assertaining confidence intervals for a limited validation sample.

A friend of mine came up with a solution in which I keep all the accuracy outputs in a vector and plot them like a histogram (I cant seem to paste one into this reply window but can send it over if necessary by email).

Thank you for the quick reply. The method I am currently using is subsampling. Randomly selecting different observations for the training set and the validation set 50 times, and collecting the accuracy scores to make a distribution of accuracy scores. I believe this is called subsampling. But I am happy to use bootstrapping instead.

Just to clarify, I am using the bootstrap on the data for partitioning the training and validation set correct? This means that an observation in the training set can also end up in the validation set.

But typically when I check the mean of the resample, mean(model$resample$Accuracy), the mean is lower than the k=5 accuracy (typically 0.65). Is there a reason for this? I would have thought that the mean accuracy of the best tune resamples would equal the model accuracy in the results.

Probably using on the standard deviation of the error score, from the mean, e.g. +/- 2 or 3 standard deviations will cover the expected behaviour of the system: https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule

I have a neural network(MLP) for binary classification with a logistic output between 0 and 1. With each run, I have to adjust my threshold on test set for minimizing the misclassifications. My question is to present my results, should I run it multiple times, adjust threshold each time and then take the average of other metrics eg F1 score or I dont optimize for the threshold at all?

I would take the test as an evaluation of the system that includes the model and automatic threshold adjusting procedure. In that case, averaging the results of the whole system is reasonable, as long as you clearly state that is what you are doing.

Lets say I have run a repeated (10) 10-cross validation experiment with predictions implemented via a Markov chain model. As a measure of robustness, I want to compute the SD of the AUC across the runs/folders for the test set.

Wilson score is different, the one youre describing is Normal approximation interval according to Wikipedia https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Normal_approximation_interval

I have come across a few posts/slides around CLT which state that in order for the sample proportion (or mean or error rate) of a binomial distribution to approximate to normal distribution (to compute confidence interval), it should follow below 2 conditions: np > 10 n(1-p) > 10 ex ref. http://homepages.math.uic.edu/~bpower6/stat101/Sampling%20Distributions.pdf

How to compute CI with cross-validation? Do we use the CI on mean results? the n value is the test portion or the sum of then? Tne formula used in https://scikit-learn.org/stable/modules/cross_validation.html#computing-cross-validated-metrics , by multiplying std * 2 was unclear.

Perhaps a unreliable estimate, there is a reference or paper/book where this formula came from? cross-val will give me [acc1, acc2,acc3, acc30] list with accuracys and I just comput the mean +/- 2 * std to represent the C.I. (CI = 2* std). What about n value, or 1.96 z value?

Step one Split train/validation 80/20 and use the train (80%) into cross-validation to get perfoemance metrics to show as means and std. Step two Train a final model with bootstrap on 20% left and comput performances with confifence intervals.

how to compute confidence measure for svm classifiers | perpetual enigma

how to compute confidence measure for svm classifiers | perpetual enigma

Support Vector Machines are machine learning models that are used to classify data. Lets say you want to build a system that can automatically identify if the input image contains a given object. For ease of understanding, lets limit the discussion to three different types of objects i.e. chair, laptop, and refrigerator. To build this, we need to collect images of chairs, laptops, and refrigerators so that our system can learn what these objects look like. Once it learns that, it can tell us whether an unknown image contains a chair or a laptop or a refrigerator. SVMs are great at this task! Even though it can predict the output, wouldnt it be nice if we knew how confident it is about the prediction? This would really help us in designing a robust system. So how do wecompute these confidence measures?

This discussion is specifically related to scikit-learn. It is a famous Python library thats used extensively to build machine learning systems. It offers a variety of algorithms and tools that are useful to developthesesystems. Lets quickly build an SVM to get started:

We can clearly see that the datapoints can be divided into two groups. Now, lets say there is a new datapoint like [1, 3] and we want to predict which class it belongs to. We just need to run the following command:

Although we know which class it belongs to, we dont know how farit is from the boundary. Lets consider two points, say [4, 2] and [1, 0]. If you plot these points on the graph, we can confidently say that [1, 0] belongs to class 0. But [4, 2] lies right on the boundaryand we are not so sure where its going to go. So we need a way to quantify this! To do that, we have a function called decision_function that computes the signed distance of a point from the boundary. A negative value would indicate class 0 and a positive value would indicate class 1. Also, a value close to 0 would indicate that the point is close to the boundary.

Not exactly! In the above example, decision_function computes the distance from the boundary but its not the same as computing the probability that a given datapoint belongs to a particular class. To do that, we need to use predict_proba. This method computes the probability that a given datapoint belongs to a particular class using Platt scaling. You can check out the original paper by Platt here. Basically, Platt scaling computes the probabilities using the following method:

Here, P(class/input) is the probability that input belongs to class and f(input) is the signed distance of the input datapoint from the boundary, which is basically the output of decision_function. We need to train the SVM as usual and then optimize the parameters A and B. The value of P(class/input) will always be between 0 and 1. Bear in mind that the training method would be slightly different if we want to use Platt scaling. We need to train a probability model on top of our SVM. Also, to avoid overfitting, it uses n-fold cross validation. So this is a lot more expensive than training a non-probabilistic SVM (like we did earlier). Lets see how to do it:

It is43.25% sure that it belongs to class 0 and 56.74% sure that it belongs to class 1. As we can see, the decision is not very clear,which seems fair given the fact that this point is close to the boundary. Looks like we are all set!

classification - how to calculate the confidence of a classifier's output? - artificial intelligence stack exchange

classification - how to calculate the confidence of a classifier's output? - artificial intelligence stack exchange

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Obvious answer for a binary (2 classes)classification is .5. Beyond that the earlier comment is correct. One of the things I have seen done is to run your model on the test set and save the prediction probability results. Then create a threshold variable call it thresh. Then increment thresh from 0 to 1 in a loop. On each iteration compare thresh with the highest predicted probability prediction call it P. If P>thresh declare that as the selected prediction, then compare that with the true prediction. Keep track of the errors for each value of thresh. At the end select the value of thresh that has the least errors. There are also some more sophisticated methods for example "top 2 accuracy" where thresh is selected based on having the true class within either the prediction with the highest probability or the second highest probability . You can construct a weighted error function and select the value of thresh that has the net lowest error over the test set. For example an error function might be as follows. If neither P(highest) or P(second highest) = True class, error=1. If P(second highest) = true class, error=.5. If p(highest)=true class error=0. I have never tried this myself so I am not sure how well this works. When I get some time will try it on a model with 100 classes and see how well it does. I know in the Imagenet competition they evaluate not just the top accuracy but also the "Top 3" and "Top 5' accuracy. In that competition there are 1000 classes. I never thought of this before but I assume you could train your model specifically to optimize say the Top 2 accuracy by constructing a loss function used during training that forces the network to minimize this loss.

Basically, the Softmax will produce a set of probabilities that all sum up to 1. So if you have three classes in your data the Softmax will produce these confidence values by default, even though this is not exactly its main functionality.

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dynamic classifier ensemble using classification confidence - sciencedirect

dynamic classifier ensemble using classification confidence - sciencedirect

How to combine the outputs from base classifiers is a key issue in ensemble learning. This paper presents a dynamic classifier ensemble method termed as DCE-CC. It dynamically selects a subset of classifiers for test samples according to classification confidence. The weights of base classifiers are learned by optimization of margin distribution on the training set, and the ordered aggregation technique is exploited to estimate the size of an appropriate subset. We examine the proposed fusion method on some benchmark classification tasks, where the stable nearest-neighbor rule and the unstable C4.5 decision tree algorithm are used for generating base classifiers, respectively. Compared with some other multiple classifier fusion algorithms, the experimental results show the effectiveness of our approach. Then we explain the experimental results from the view point of margin distribution.

Leijun Li got his B.Sc., M.Sc. from Hebei Normal University in 2007 and 2010, respectively. Now he is a Ph.D. candidate with School of Computer Science and Technology, Harbin Institute of Technology. His research interests include ensemble learning, margin theory and rough sets, etc.

Bo Zou got his B.Sc., M.E. and Ph.D. degrees from Harbin Institute of Technology, Harbin, China in 2001, 2005 and 2009, respectively. He was a postdoctoral fellow with School of Economics and Management from 2009 to 2011. Now he is an associate professor with this school. His main interests are knowledge management, knowledge discovery and data mining.

Qinghua Hu received B.Sc., M.E. and Ph.D. degrees from Harbin Institute of Technology, Harbin, China in 1999, 2002 and 2008, respectively. He started working with Harbin Institute of Technology from 2006, and was a postdoctoral fellow with the Hong Kong Polytechnic University from 2009 to 2011. Now he is a full professor with Tianjin University. His research interests are focused on intelligent modeling, data mining, knowledge discovery for classification and regression. He is a PC co-chair of RSCTC 2010 and severs as referee for a great number of journals and conferences. He has published more than 90 journal and conference papers in the areas of pattern recognition and fault diagnosis.

Xianqian Wu received his B.Sc., M.E. and Ph.D. degrees from Harbin Institute of Technology, Harbin, China in 1997, 1999 and 2004, respectively. Now he is a full professor with School of Computer Science and Technology, Harbin Institute of Technology. He once visited The Hong Kong Polytechnic University and Michigan State University. His main interests are focused on biometrics, image processing and pattern recognition. He has published more than 50 peer revived papers in these domains.

Daren Yu received the M.Sc. and D.Sc. degrees from Harbin Institute of Technology, Harbin, China, in 1988 and 1996, respectively. Since 1988, he has been working at the School of Energy Science and Engineering, Harbin Institute of Technology. His main research interests are in modeling, simulation, and control of power systems. He has published more than one hundred conference and journal papers on power control and fault diagnosis.

classifier combination based on confidence transformation - sciencedirect

classifier combination based on confidence transformation - sciencedirect

This paper investigates the effects of confidence transformation in combining multiple classifiers using various combination rules. The combination methods were tested in handwritten digit recognition by combining varying classifier sets. The classifier outputs are transformed to confidence measures by combining three scaling functions (global normalization, Gaussian density modeling, and logistic regression) and three confidence types (linear, sigmoid, and evidence). The combination rules include fixed rules (sum-rule, product-rule, median-rule, etc.) and trained rules (linear discriminants and weighted combination with various parameter estimation techniques). The experimental results justify that confidence transformation benefits the combination performance of either fixed rules or trained rules. Trained rules mostly outperform fixed rules, especially when the classifier set contains weak classifiers. Among the trained rules, the support vector machine with linear kernel (linear SVM) performs best while the weighted combination with optimized weights performs comparably well. I have also attempted the joint optimization of confidence parameters and combination weights but its performance was inferior to that of cascaded confidence transformation-combination. This justifies that the cascaded strategy is a right way of multiple classifier combination.

About the AuthorCHENG-LIN LIU received the B.S. degree in electronic engineering from Wuhan University, Wuhan, China, the M.E. degree in electronic engineering from Beijing Polytechnic University, Beijing, China, the Ph.D. degree in pattern recognition and artificial intelligence from the Institute of Automation, Chinese Academy of Sciences, Beijing, China, in 1989, 1992 and 1995, respectively. From March 1996 to March 1999, he was a postdoctoral fellow in Korea Advanced Institute of Science and Technology (KAIST), Taejon, Korea, and later in Tokyo University of Agriculture and Technology, Tokyo, Japan. Afterwards, he became a research staff member at the Central Research Laboratory, Hitachi, Ltd., Tokyo, Japan, where he was promoted to a senior researcher in 2002. His research interests include pattern recognition, artificial intelligence, image processing, neural networks, machine learning, and especially the applications to character recognition and document processing.

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