Incremental Training of a Detector Using Online Sparse Eigen-decomposition

The ability to efficiently and accurately detect objects plays a very crucial role for many computer vision tasks. Recently, offline object detectors have shown a tremendous success. However, one major drawback of offline techniques is that a complete set of training data has to be collected beforehand. In addition, once learned, an offline detector can not make use of newly arriving data. To alleviate these drawbacks, online learning has been adopted with the following objectives: (1) the technique should be computationally and storage efficient; (2) the updated classifier must maintain its high classification accuracy. In this paper, we propose an effective and efficient framework for learning an adaptive online greedy sparse linear discriminant analysis (GSLDA) model. Unlike many existing online boosting detectors, which usually apply exponential or logistic loss, our online algorithm makes use of LDA's learning criterion that not only aims to maximize the class-separation criterion but also incorporates the asymmetrical property of training data distributions. We provide a better alternative for online boosting algorithms in the context of training a visual object detector. We demonstrate the robustness and efficiency of our methods on handwriting digit and face data sets. Our results confirm that object detection tasks benefit significantly when trained in an online manner.Comment: 14 page

Boosting alternating decision trees modeling of disease trait information

We applied the alternating decision trees (ADTrees) method to the last 3 replicates from the Aipotu, Danacca, Karangar, and NYC populations in the Problem 2 simulated Genetic Analysis Workshop dataset. Using information from the 12 binary phenotypes and sex as input and Kofendrerd Personality Disorder disease status as the outcome of ADTrees-based classifiers, we obtained a new quantitative trait based on average prediction scores, which was then used for genome-wide quantitative trait linkage (QTL) analysis. ADTrees are machine learning methods that combine boosting and decision trees algorithms to generate smaller and easier-to-interpret classification rules. In this application, we compared four modeling strategies from the combinations of two boosting iterations (log or exponential loss functions) coupled with two choices of tree generation types (a full alternating decision tree or a classic boosting decision tree). These four different strategies were applied to the founders in each population to construct four classifiers, which were then applied to each study participant. To compute average prediction score for each subject with a specific trait profile, such a process was repeated with 10 runs of 10-fold cross validation, and standardized prediction scores obtained from the 10 runs were averaged and used in subsequent expectation-maximization Haseman-Elston QTL analyses (implemented in GENEHUNTER) with the approximate 900 SNPs in Hardy-Weinberg equilibrium provided for each population. Our QTL analyses on the basis of four models (a full alternating decision tree and a classic boosting decision tree paired with either log or exponential loss function) detected evidence for linkage (Z ≥ 1.96, p < 0.01) on chromosomes 1, 3, 5, and 9. Moreover, using average iteration and abundance scores for the 12 phenotypes and sex as their relevancy measurements, we found all relevant phenotypes for all four populations except phenotype b for the Karangar population, with suggested subgroup structure consistent with latent traits used in the model. In conclusion, our findings suggest that the ADTrees method may offer a more accurate representation of the disease status that allows for better detection of linkage evidence

Comment: Boosting Algorithms: Regularization, Prediction and Model Fitting

The authors are doing the readers of Statistical Science a true service with a well-written and up-to-date overview of boosting that originated with the seminal algorithms of Freund and Schapire. Equally, we are grateful for high-level software that will permit a larger readership to experiment with, or simply apply, boosting-inspired model fitting. The authors show us a world of methodology that illustrates how a fundamental innovation can penetrate every nook and cranny of statistical thinking and practice. They introduce the reader to one particular interpretation of boosting and then give a display of its potential with extensions from classification (where it all started) to least squares, exponential family models, survival analysis, to base-learners other than trees such as smoothing splines, to degrees of freedom and regularization, and to fascinating recent work in model selection. The uninitiated reader will find that the authors did a nice job of presenting a certain coherent and useful interpretation of boosting. The other reader, though, who has watched the business of boosting for a while, may have quibbles with the authors over details of the historic record and, more importantly, over their optimism about the current state of theoretical knowledge. In fact, as much as ``the statistical view'' has proven fruitful, it has also resulted in some ideas about why boosting works that may be misconceived, and in some recommendations that may be misguided. [arXiv:0804.2752]Comment: Published in at http://dx.doi.org/10.1214/07-STS242B the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Proximal boosting and its acceleration

Gradient boosting is a prediction method that iteratively combines weak learners to produce a complex and accurate model. From an optimization point of view, the learning procedure of gradient boosting mimics a gradient descent on a functional variable. This paper proposes to build upon the proximal point algorithm when the empirical risk to minimize is not differentiable to introduce a novel boosting approach, called proximal boosting. Besides being motivated by non-differentiable optimization, the proposed algorithm benefits from Nesterov's acceleration in the same way as gradient boosting [Biau et al., 2018]. This leads to a variant, called accelerated proximal boosting. Advantages of leveraging proximal methods for boosting are illustrated by numerical experiments on simulated and real-world data. In particular, we exhibit a favorable comparison over gradient boosting regarding convergence rate and prediction accuracy