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34
An Active Testing Model for Tracking Roads in Satellite Images
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1995
"... We present a new approach for tracking roads from satellite images, and thereby illustrate a general computational strategy ("active testing") for tracking 1D structures and other recognition tasks in computer vision. Our approach is related to recent work in active vision on "where ..."
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Cited by 159 (5 self)
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We present a new approach for tracking roads from satellite images, and thereby illustrate a general computational strategy ("active testing") for tracking 1D structures and other recognition tasks in computer vision. Our approach is related to recent work in active vision on "where to look next" and motivated by the "divideandconquer" strategy of parlor games such as "Twenty Questions." We choose "tests" (matched filters for short road segments) one at a time in order to remove as much uncertainty as possible about the "true hypothesis" (road position) given the results of the previous tests. The tests are chosen online based on a statistical model for the joint distribution of tests and hypotheses. The problem of minimizing uncertainty (measured by entropy) is formulated in simple and explicit analytical terms. To execute this entropy testing rule we then alternate between data collection and optimization: at each iteration new image data are examined and a new entropy minimizat...
The Power of Decision Tables
 Proceedings of the European Conference on Machine Learning
, 1995
"... . We evaluate the power of decision tables as a hypothesis space for supervised learning algorithms. Decision tables are one of the simplest hypothesis spaces possible, and usually they are easy to understand. Experimental results show that on artificial and realworld domains containing only discre ..."
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Cited by 107 (5 self)
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. We evaluate the power of decision tables as a hypothesis space for supervised learning algorithms. Decision tables are one of the simplest hypothesis spaces possible, and usually they are easy to understand. Experimental results show that on artificial and realworld domains containing only discrete features, IDTM, an algorithm inducing decision tables, can sometimes outperform stateoftheart algorithms such as C4.5. Surprisingly, performance is quite good on some datasets with continuous features, indicating that many datasets used in machine learning either do not require these features, or that these features have few values. We also describe an incremental method for performing crossvalidation that is applicable to incremental learning algorithms including IDTM. Using incremental crossvalidation, it is possible to crossvalidate a given dataset and IDTM in time that is linear in the number of instances, the number of features, and the number of label values. The time for incre...
Hierarchical testing designs for pattern recognition
, 2003
"... We explore the theoretical foundations of a “twenty questions” approach to pattern recognition. The object of the analysis is the computational process itself rather than probability distributions (Bayesian inference) or decision boundaries (statistical learning). Our formulation is motivated by app ..."
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Cited by 38 (8 self)
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We explore the theoretical foundations of a “twenty questions” approach to pattern recognition. The object of the analysis is the computational process itself rather than probability distributions (Bayesian inference) or decision boundaries (statistical learning). Our formulation is motivated by applications to scene interpretation in which there are a great many possible explanations for the data, one (“background”) is statistically dominant, and it is imperative to restrict intensive computation to genuinely ambiguous regions. The focus here is then on pattern filtering: Given a large set Y of possible patterns or explanations, narrow down the true one Y to a small (random) subset ̂Y ⊂ Y of “detected ” patterns to be subjected to further, more intense, processing. To this end, we consider a family of hypothesis tests for Y ∈ A versus the nonspecific alternatives Y ∈ A c. Each test has null type I error and the candidate sets A ⊂ Y are arranged in a hierarchy of nested partitions. These tests are then
Decision Trees For Geometric Models
, 1993
"... A fundamental problem in modelbased computer vision is that of identifying which of a given set of geometric models is present in an image. Considering a "probe" to be an oracle that tells us whether or not a model is present at a given point, we study the problem of computing efficien ..."
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Cited by 32 (4 self)
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A fundamental problem in modelbased computer vision is that of identifying which of a given set of geometric models is present in an image. Considering a "probe" to be an oracle that tells us whether or not a model is present at a given point, we study the problem of computing efficient strategies ("decision trees") for probing an image, with the goal to minimize the number of probes necessary (in the worst case) to determine which single model is present. We show that a dlg ke height binary decision tree always exists for k polygonal models (in fixed position), provided (1) they are nondegenerate (do not share boundaries) and (2) they share a common point of intersection. Further, we give an efficient algorithm for constructing such decision tress when the models are given as a set of polygons in the plane. We show that constructing a minimum height tree is NPcomplete if either of the two assumptions is omitted. We provide an efficient greedy heuristic strategy and show ...
Performance bounds on the splitting algorithm for binary testing
 Acta Informatica
, 1974
"... Summary. In machine faultlocation, medical diagnosis, species identification, and computer decisionmaking, one is often required to identify some unknown object or condition, belonging to a known set of M possibilities, by applying a sequence of binaryvalued tests, which are selected from a given ..."
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Cited by 22 (0 self)
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Summary. In machine faultlocation, medical diagnosis, species identification, and computer decisionmaking, one is often required to identify some unknown object or condition, belonging to a known set of M possibilities, by applying a sequence of binaryvalued tests, which are selected from a given set of available tests. One would usually prefer such a testing procedure which minimizes or nearly minimizes the expected testing cost for identification. Existing methods for determining a minimal expected cost testing procedure, however, require a number of operations which increases exponentially with M and become infeasible for solving problems of even moderate size. Thus, in practice, one instead uses fast, heuristic methods which hopefully obtain low cost testing procedures, but which do not guarantee a minimal cost solution. Examining the important case in which all M possibilities are equally likely, we derive a number of costbounding results for the most common heuristic procedure, which always applies next that test yielding maximum information gain per unit cost. In particular, we show that solutions obtained using this method can have expected cost greater than an arbitrary multiple of the optimal expected cost.
Mining Optimal Decision Trees from Itemset Lattices
, 2007
"... We present an exact algorithm for finding a decision tree that optimizes a ranking function under size, depth, accuracy and leaf constraints. Because the discovery of optimal trees has high theoretical complexity, until now no efforts have been made to compute such trees for realworld datasets. An ..."
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Cited by 11 (5 self)
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We present an exact algorithm for finding a decision tree that optimizes a ranking function under size, depth, accuracy and leaf constraints. Because the discovery of optimal trees has high theoretical complexity, until now no efforts have been made to compute such trees for realworld datasets. An exact algorithm is of both scientific and practical interest. From the scientific point of view, it can be used as a gold standard to evaluate the performance of heuristic decision tree learners, and it can be used to gain new insight in traditional decision tree learners. From the application point of view, it can be used to discover trees that cannot be found by heuristic decision tree learners. The key idea behind our algorithm is the relation between constraints on decision trees and constraints on itemsets. We propose to exploit lattices of itemsets, from which we can extract optimal decision trees in linear time. We give several strategies to efficiently build these lattices and show that the test set accuracies of C4.5 compete with the test set accuracies of optimal trees.
Approximating Optimal Binary Decision Trees
"... Abstract. We give a (ln n + 1)approximation for the decision tree (DT) problem. We also show that DT does not have a PTAS unless P=NP. An instance of DT is a set of m binary tests T = (T1,..., Tm) and a set of n items X = (X1,..., Xn). The goal is to output a binary tree where each internal node is ..."
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Cited by 10 (0 self)
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Abstract. We give a (ln n + 1)approximation for the decision tree (DT) problem. We also show that DT does not have a PTAS unless P=NP. An instance of DT is a set of m binary tests T = (T1,..., Tm) and a set of n items X = (X1,..., Xn). The goal is to output a binary tree where each internal node is a test, each leaf is an item and the total external path length of the tree is minimized. DT has a rich history in computer science with applications ranging from medical diagnosis to experiment design. Our work, while providing the first nontrivial upper and lower bounds on approximating DT, also demonstrates that DT and a subtly different problem which also bears the name decision tree (but which we call ConDT) have fundamentally different approximation complexity. We conclude with a stronger lower bound for a third decision tree problem called MinDT. 1
Sequential Decision Models for Expert System Optimization
 IEEE Transactions on Knowledge and Data Engineering
, 1997
"... ..."
Efficient Monitoring of ωlanguages
, 2005
"... We present a technique for generating efficient monitors for ωregularlanguages. We show how Büchi automata can be reduced in size and transformed into special, statistically optimal nondeterministic finite state machines, called binary transition tree finite state machines (BTTFSMs), which recogn ..."
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Cited by 8 (0 self)
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We present a technique for generating efficient monitors for ωregularlanguages. We show how Büchi automata can be reduced in size and transformed into special, statistically optimal nondeterministic finite state machines, called binary transition tree finite state machines (BTTFSMs), which recognize precisely the minimal bad prefixes of the original ωregularlanguage. The presented technique is implemented as part of a larger monitoring framework and is available for download.
ModelBased Classification Trees
 IEEE Transactions on Information Theory
, 1998
"... The construction of classification trees is nearly always topdown, locally optimal and datadriven. Such recursive designs are often globally inefficient, for instance in terms of the mean depth necessary to reach a given classification rate. We consider statistical models for which exact global op ..."
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Cited by 7 (2 self)
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The construction of classification trees is nearly always topdown, locally optimal and datadriven. Such recursive designs are often globally inefficient, for instance in terms of the mean depth necessary to reach a given classification rate. We consider statistical models for which exact global optimization is feasible, and thereby demonstrate that recursive and global procedures may result in very different tree graphs and overall performance. Keywords. Classification tree, optimal testing strategy, dynamic programming, pattern recognition. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003; Email:geman@math.umass.edu. Supported in part by the NSF under grant DMS9217655, ONR under contract N000149710249, Army Research Office under MURI grant DAAH049610445, y D'epartement de probabilit'es et statistiques, Universit'e des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex; Email:Bruno.Jedynak@univlille1.fr 1 Introductio...