13,412 research outputs found
Doubly Optimized Calibrated Support Vector Machine (DOC-SVM): an algorithm for joint optimization of discrimination and calibration.
Historically, probabilistic models for decision support have focused on discrimination, e.g., minimizing the ranking error of predicted outcomes. Unfortunately, these models ignore another important aspect, calibration, which indicates the magnitude of correctness of model predictions. Using discrimination and calibration simultaneously can be helpful for many clinical decisions. We investigated tradeoffs between these goals, and developed a unified maximum-margin method to handle them jointly. Our approach called, Doubly Optimized Calibrated Support Vector Machine (DOC-SVM), concurrently optimizes two loss functions: the ridge regression loss and the hinge loss. Experiments using three breast cancer gene-expression datasets (i.e., GSE2034, GSE2990, and Chanrion's datasets) showed that our model generated more calibrated outputs when compared to other state-of-the-art models like Support Vector Machine (p=0.03, p=0.13, and p<0.001) and Logistic Regression (p=0.006, p=0.008, and p<0.001). DOC-SVM also demonstrated better discrimination (i.e., higher AUCs) when compared to Support Vector Machine (p=0.38, p=0.29, and p=0.047) and Logistic Regression (p=0.38, p=0.04, and p<0.0001). DOC-SVM produced a model that was better calibrated without sacrificing discrimination, and hence may be helpful in clinical decision making
Stratification bias in low signal microarray studies
BACKGROUND:
When analysing microarray and other small sample size biological datasets, care is needed to avoid various biases. We analyse a form of bias, stratification bias, that can substantially affect analyses using sample-reuse validation techniques and lead to inaccurate results. This bias is due to imperfect stratification of samples in the training and test sets and the dependency between these stratification errors, i.e. the variations in class proportions in the training and test sets are negatively correlated.
RESULTS:
We show that when estimating the performance of classifiers on low signal datasets (i.e. those which are difficult to classify), which are typical of many prognostic microarray studies, commonly used performance measures can suffer from a substantial negative bias. For error rate this bias is only severe in quite restricted situations, but can be much larger and more frequent when using ranking measures such as the receiver operating characteristic (ROC) curve and area under the ROC (AUC). Substantial biases are shown in simulations and on the van 't Veer breast cancer dataset. The classification error rate can have large negative biases for balanced datasets, whereas the AUC shows substantial pessimistic biases even for imbalanced datasets. In simulation studies using 10-fold cross-validation, AUC values of less than 0.3 can be observed on random datasets rather than the expected 0.5. Further experiments on the van 't Veer breast cancer dataset show these biases exist in practice.
CONCLUSION:
Stratification bias can substantially affect several performance measures. In computing the AUC, the strategy of pooling the test samples from the various folds of cross-validation can lead to large biases; computing it as the average of per-fold estimates avoids this bias and is thus the recommended approach. As a more general solution applicable to other performance measures, we show that stratified repeated holdout and a modified version of k-fold cross-validation, balanced, stratified cross-validation and balanced leave-one-out cross-validation, avoids the bias. Therefore for model selection and evaluation of microarray and other small biological datasets, these methods should be used and unstratified versions avoided. In particular, the commonly used (unbalanced) leave-one-out cross-validation should not be used to estimate AUC for small datasets
Convex Optimization for Binary Classifier Aggregation in Multiclass Problems
Multiclass problems are often decomposed into multiple binary problems that
are solved by individual binary classifiers whose results are integrated into a
final answer. Various methods, including all-pairs (APs), one-versus-all (OVA),
and error correcting output code (ECOC), have been studied, to decompose
multiclass problems into binary problems. However, little study has been made
to optimally aggregate binary problems to determine a final answer to the
multiclass problem. In this paper we present a convex optimization method for
an optimal aggregation of binary classifiers to estimate class membership
probabilities in multiclass problems. We model the class membership probability
as a softmax function which takes a conic combination of discrepancies induced
by individual binary classifiers, as an input. With this model, we formulate
the regularized maximum likelihood estimation as a convex optimization problem,
which is solved by the primal-dual interior point method. Connections of our
method to large margin classifiers are presented, showing that the large margin
formulation can be considered as a limiting case of our convex formulation.
Numerical experiments on synthetic and real-world data sets demonstrate that
our method outperforms existing aggregation methods as well as direct methods,
in terms of the classification accuracy and the quality of class membership
probability estimates.Comment: Appeared in Proceedings of the 2014 SIAM International Conference on
Data Mining (SDM 2014
Online Robot Introspection via Wrench-based Action Grammars
Robotic failure is all too common in unstructured robot tasks. Despite
well-designed controllers, robots often fail due to unexpected events. How do
robots measure unexpected events? Many do not. Most robots are driven by the
sense-plan act paradigm, however more recently robots are undergoing a
sense-plan-act-verify paradigm. In this work, we present a principled
methodology to bootstrap online robot introspection for contact tasks. In
effect, we are trying to enable the robot to answer the question: what did I
do? Is my behavior as expected or not? To this end, we analyze noisy wrench
data and postulate that the latter inherently contains patterns that can be
effectively represented by a vocabulary. The vocabulary is generated by
segmenting and encoding the data. When the wrench information represents a
sequence of sub-tasks, we can think of the vocabulary forming a sentence (set
of words with grammar rules) for a given sub-task; allowing the latter to be
uniquely represented. The grammar, which can also include unexpected events,
was classified in offline and online scenarios as well as for simulated and
real robot experiments. Multiclass Support Vector Machines (SVMs) were used
offline, while online probabilistic SVMs were are used to give temporal
confidence to the introspection result. The contribution of our work is the
presentation of a generalizable online semantic scheme that enables a robot to
understand its high-level state whether nominal or abnormal. It is shown to
work in offline and online scenarios for a particularly challenging contact
task: snap assemblies. We perform the snap assembly in one-arm simulated and
real one-arm experiments and a simulated two-arm experiment. This verification
mechanism can be used by high-level planners or reasoning systems to enable
intelligent failure recovery or determine the next most optima manipulation
skill to be used.Comment: arXiv admin note: substantial text overlap with arXiv:1609.0494
- …