1779699
Hidden Naive Bayes
The conditional independence assumption of naive Bayes essentially ignores attribute dependencies and is often violated. On the other hand, although a Bayesian network can represent arbitrary attribute dependencies, learning an optimal Bayesian network from data is intractable. The main reason is that learning the optimal structure of a Bayesian network is extremely time consuming. Thus, a Bayesian model without structure learning is desirable. In this paper, we propose a novel model, called hidden naive Bayes (HNB). In an HNB, a hidden parent is created for each attribute which combines the influences from all other attributes. We present an approach to creating hidden parents using the average of weighted one-dependence estimators. HNB inherits the structural simplicity of naive Bayes and can be easily learned without structure learning. We propose an algorithm for learning HNB based on conditional mutual information. We experimentally test HNB in terms of classification accuracy, using the 36 UCI data sets recommended by Weka (Witten & Frank 2000), and compare it to naive Bayes (Langley, Iba, & Thomas 1992), C4.5 (Quinlan 1993), SBC (Langley & Sage 1994), NBTree (Kohavi 1996), CL-TAN (Friedman, Geiger, & Goldszmidt 1997), and AODE (Webb, Boughton, & Wang 2005). The experimental results show that HNB outperforms naive Bayes, C4.5, SBC, NBTree, and CL-TAN, and is competitive with AODE.
139220
Representational Upper Bounds of Bayesian Networks
One of the fundamental issues of Bayesian networks is their representational power, re-ecting what kind of functions they can or cannot represent. In this paper, we rst prove an upper bound on the representational power of Augmented Naive Bayes. We then extend the result to general Bayesian networks. Roughly speaking, if a function contains an m-XOR, there exists no Bayesian networks with node having at most m ? 1 parents to represent it.
7586705
The Representational Power of Discrete Bayesian Networks
One of the most important fundamental properties of Bayesian networks is the representational power, reflecting what kind of functions they can or cannot represent. In this paper, we establish an association between the structural complexity of Bayesian networks and their representational power. We use the maximum number of nodes' parents as the measure for the structural complexity of Bayesian networks, and the maximum XOR contained in a target function as the measure for the function complexity. A representational upper bound is established and proved. Roughly speaking, discrete Bayesian networks with each node having at most k parents cannot represent any function containing (k+1)-XORs. Our theoretical results help us to gain a deeper understanding on the capacities and limitations of Bayesian networks.
5976625
Augmenting naive Bayes for ranking
Naive Bayes is an effective and efficient learning algorithm in classification. In many applications, however, an accurate ranking of instances based on the class probability is more desirable. Unfortunately, naive Bayes has been found to produce poor probability estimates. Numerous techniques have been proposed to extend naive Bayes for better classification accuracy, of which selective Bayesian classifiers (SBC) (Langley & Sage, 1994), tree-augmented naive Bayes (TAN) (Friedman et al., 1997), NBTree (Kohavi, 1996), boosted naive Bayes (Elkan, 1997), and AODE (Webb et al., 2005) achieve remarkable improvement over naive Bayes in terms of classification accuracy. An interesting question is: Do these techniques also produce accurate ranking? In this paper, we first conduct a systematic experimental study on their efficacy for ranking. Then, we propose a new approach to augmenting naive Bayes for generating accurate ranking, called hidden naive Bayes (HNB). In an HNB, a hidden parent is created for each attribute to represent the influences from all other attributes, and thus a more accurate ranking is expected. HNB inherits the structural simplicity of naive Bayes and can be easily learned without structure learning. Our experiments show that HNB outperforms naive Bayes, SBC, boosted naive Bayes, NBTree, and TAN significantly, and performs slightly better than AODE in ranking.
2128098
A Fast Decision Tree Learning Algorithm
There is growing interest in scaling up the widely-used decision-tree learning algorithms to very large data sets. Although numerous diverse techniques have been proposed, a fast tree-growing algorithm without substantial decrease in accuracy and substantial increase in space complexity is essential. In this paper, we present a novel, fast decision-tree learning algorithm that is based on a conditional independence assumption. The new algorithm has a time complexity of O(m ċ n), where m is the size of the training data and n is the number of attributes. This is a significant asymptotic improvement over the time complexity O(m ċ n2) of the standard decision-tree learning algorithm C4.5, with an additional space increase of only O(n). Experiments show that our algorithm performs competitively with C4.5 in accuracy on a large number of UCI benchmark data sets, and performs even better and significantly faster than C4.5 on a large number of text classification data sets. The time complexity of our algorithm is as low as naive Bayes'. Indeed, it is as fast as naive Bayes but outperforms naive Bayes in accuracy according to our experiments. Our algorithm is a core tree-growing algorithm that can be combined with other scaling-up techniques to achieve further speedup.
13845864
On the interaction between overlay routing and underlay routing
In this paper, we study the interaction between overlay routing and traffic engineering (TE) in a single autonomous system (AS). We formulate this interaction as a two-player non-cooperative non-zero sum game, where the overlay tries to minimize the delay of its traffic and the TE's objective is to minimize network cost. We study a Nash routing game with best-reply dynamics, in which the overlay and TE have equal status, and take turns to compute their optimal strategies based on the response of the other player in the previous round. We prove the existence, uniqueness and global stability of Nash equilibrium point (NEP) for a simple network. For general networks, we show that the selfish behavior of an overlay can cause huge cost increases and oscillations to the whole network. Even worse, we have identified cases, both analytically and experimentally, where the overlay's cost increases as the Nash routing game proceeds even though the overlay plays optimally based on TE's routing at each round. Experiments are performed to verify our analysis.
2899757
Providing throughput differentiation for TCP flows using adaptive two-color marking and two-level AQM
In this paper we propose a new paradigm for a Differentiated Service (DiffServ) network consisting of two-color marking at the edges of the network using token buckets coupled with differential treatment in the core. Using fluid-flow modelling, we present existence conditions for token-bucket rates and differential marking probabilities at the core that result in all edges receiving at least their minimum guaranteed rates. We then present an integrated DiffServ architecture comprising of an active rate management controller at the marking edge and a two-level active queue management controller at the core. The validity of the fluid flow model and performance of this new scheme are verified using ns simulations.
564702
A hidden environment model for constructing indoor radio maps
Constructing indoor radio maps plays an important role in many services and applications, such as wireless base station planning. We propose a hybrid approach to constructing indoor radio maps by developing a novel indoor signal propagation model, called the hidden environment model (HEM). The model is hybrid because it combines on-site measurements with a number of different types of calculations. As part of this model, we introduce the idea of an environment factor matrix (EFM). The EFM represents a model of the environmental features that affect radio attenuation. We also develop a lazy sampling algorithm to help generate the EFM. The goal of the lazy sampling algorithm is to balance the number of measurements that need to be taken with our model's accuracy. The goal is to minimize the measurement workload while maintaining satisfactory accuracy. We evaluate our model by comparing the radio maps calculated from the model to a radio map obtained by exhaustive measurements. The results show that our hidden environment model achieves good accuracy.
1131614
Meta-Evaluation of Image Segmentation Using Machine Learning
Image segmentation is a fundamental step in many computer vision applications. Generally, the choice of a segmentation algorithm, or parameterization of a given algorithm, is selected at the application level and fixed for all images within that application. Our goal is to create a stand-alone method to evaluate segmentation quality. Stand-alone methods have the advantage that they do not require a manually-segmented reference image for comparison, and can therefore be used for real-time evaluation. Current stand-alone evaluation methods often work well for some types of images, but poorly for others. We propose a meta-evaluation method in which any set of base evaluation methods are combined by a machine learning algorithm that coalesces their evaluations based on a learned weighting function, which depends upon the image to be segmented. The training data used by the machine learning algorithm can be labeled by a human, based on similarity to a human-generated reference segmentation, or based upon system-level performance. Experimental results demonstrate that our method performs better than the existing stand-alone segmentation evaluation methods.
46427487
The Clar Covering Polynomial of Hexagonal Systems I
Abstract In this paper the Clar covering polynomial of a hexagonal system is introduced. In fact it is a kind of F polynomial [4] of a graph, and can be calculated by recurrence relations. We show that the number of aromatic sextets (in a Clar formula), the number of Clar formulas, the number of Kekule structures and the first Herndon number for any Kekulean hexagonal system can be easily obtained by its Clar covering polynomial. In addition, we give some theorems to calculate the Clar covering polynomial of a hexagonal system. As examples we finally derive the explicit expressions of the Clar covering polynomials for some small hexagonal systems and several types of catacondensed hexagonal systems. A relation between the resonance energy and the Clar covering polynomial of a hexagonal system is considered in the next paper.