Branch and bound | EPFL Graph Search

Branch and bound (BB, B&B, or BnB) is a method for solving optimization problems by breaking them down into smaller sub-problems and using a bounding function to eliminate sub-problems that cannot contain the optimal solution. It is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm. The algorithm depends on efficient estimation of the lower and upper bounds of re

Learning to Reduce Annotation Load

Ksenia Konyushkova

Modern machine learning methods and their applications in computer vision are known to crave for large amounts of training data to reach their full potential. Because training data is mostly obtained through humans who manually label samples, it induces a significant cost. Therefore, the problem of reducing the annotation load is of great importance for the success of machine learning methods. We study the problem of reducing the annotation load from two viewpoints, by answering the questions âWhat to annotate?â and âHow to annotate?â. The question âWhat?â addresses the selection of a small portion of the data that would be sufficient to train an accurate model. The question âHow? focuses on minimising the effort of labelling each datapoint. The question âWhat to annotate?â becomes particularly compelling if we can select data to be annotated in an iterative and adaptive way, a setting known as active learning (AL). The key challenge in AL is to identify the datapoints that are the most informative for the model at a given stage. We propose several techniques to address this challenge. Firstly, we consider the problem of segmenting natural images and image volumes. We take advantage of image priors, such as smoothness of objects of interest, and use them in a novel form of geometric uncertainty. Using this, we design an AL technique to efficiently annotate data that is tailored to segmentation applications. Next, we notice that no single manually-designed strategy outperforms others in every application and that often the burden of designing new strategies outweighs the benefits of AL. To overcome this problem we suggest learning an AL strategy from data by formulating the AL problem as a regression task that predicts the reduction in the generalisation error achieved by labelling each datapoint. This enables us to learn AL strategies from simulated data and to transfer them to new datasets. Finally, we turn towards non-myopic data-driven AL strategies. To this end, we formulate the AL problem as a Markov decision process and find the best selection policy using reinforcement learning. We design the decision process such that the policy can be learnt for any ML model and transferred to diverse application domains. Effectively addressing the question âHow to annotate?â is of no less importance as large cost savings can be achieved by labelling each datapoint more efficiently. This can be done with intelligent interfaces that interact with a human annotator. We make two contributions towards answering the question âHow?â. Firstly, we propose an efficient technique to annotate 3D image volumes for image segmentation. Annotating data in 3D is cumbersome and an obvious way to facilitate it is to select a subset of the data lying on a 2D plane. To find the optimal plane (i.e. the one containing the most informative datapoints) we design a branch-and-bound algorithm that quickly eliminates hypotheses about the optimal projection. Secondly, we propose an intelligent data annotation method to train object detectors. Instead of always asking the human annotator to draw bounding boxes in images, we detect automatically in which cases we can rely on the current detector and verify its proposal.

EPFL2019

Tracking elementary particles near their primary vertex: a combinatorial approach

Thomas Liebling

Colliding beams experiments High Energy Physics rely on solid state detectors to track the flight paths of charged elementary particles near their primary point of interaction. Reconstructing tracks in this region requires, per collision, a partitioning of up to 10^3 highly correlated observations into an unknown number of tracks. We report on the succesful implementation of a combinatorial track finding algorithm to solve this pattern recognition problem in the context of the ALEPH experiment ar CERN. Central to the implementation is a 5-dimensional axial assignment are obtained by means of an extended Kalman filter. A preprocessing step, involving the clustering and geometric partitioning of the observations, ensures reasonable bounds on the size of the poblems, which are solved using a branch & bound algorithm with LP relaxation. Convergence is reached within one second of CPU time on a RISC workstation in average.

1996

Learning to Reduce Annotation Load

Ksenia Konyushkova

EPFL2019