For classification tasks, probabilistic models can be categorized into two disjoint classes: generative or discriminative. It depends on the posterior probability computation of the label $x$ given the observation $y$, $p(x | y)$. On the one hand, generative classifiers, like the Naive Bayes or the Hidden Markov Model (HMM), need the computation of the joint probability p(x,y), before using the Bayes rule to compute $p(x | y)$. On the other hand, discriminative classifiers compute $p(x | y)$ directly, regardless of the observations' law. They are intensively used nowadays, with models as Logistic Regression, Conditional Random Fields (CRF), and Artificial Neural Networks. However, the recent Entropic Forward-Backward algorithm shows that the HMM, considered as a generative model, can also match the discriminative one's definition. This example leads to question if it is the case for other generative models. In this paper, we show that the Naive Bayes classifier can also match the discriminative classifier definition, so it can be used in either a generative or a discriminative way. Moreover, this observation also discusses the notion of Generative-Discriminative pairs, linking, for example, Naive Bayes and Logistic Regression, or HMM and CRF. Related to this point, we show that the Logistic Regression can be viewed as a particular case of the Naive Bayes used in a discriminative way.
Despite its simplicity, the naive Bayes classifier has surprised machine learning researchers by exhibiting good performance on a variety of learning problems. Encouraged by these results, researchers have looked to overcome naive Bayes primary weakness - attribute independence - and improve the performance of the algorithm. This paper presents a locally weighted version of naive Bayes that relaxes the independence assumption by learning local models at prediction time. Experimental results show that locally weighted naive Bayes rarely degrades accuracy compared to standard naive Bayes and, in…
IBM France（IBM法国）；Telecom SudParis（巴黎电信学院）；Institut Polytechnique de Paris（巴黎综合理工学院）
Naive Bayes is a popular probabilistic model appreciated for its simplicity and interpretability. However, the usual form of the related classifier suffers from two major problems. First, as caring about the observations' law, it cannot consider complex features. Moreover, it considers the conditional independence of the observations given the hidden variable. This paper introduces the original Neural Naive Bayes, modeling the parameters of the classifier induced from the Naive Bayes with neural network functions. This allows to correct the first problem. We also introduce new Neural Pooled Ma…
Naive Bayes estimator is widely used in text classification problems. However, it doesn't perform well with small-size training dataset. We propose a new method based on Naive Bayes estimator to solve this problem. A correlation factor is introduced to incorporate the correlation among different classes. Experimental results show that our estimator achieves a better accuracy compared with traditional Naive Bayes in real world data.
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；Institute for Computer Science and Control (SZTAKI), Hungarian Research Network (HUN-REN)（匈牙利研究网络计算机科学与控制研究所（SZTAKI））
Université Paris 1 Panthéon-Sorbonne（巴黎第一大学先贤祠-索邦大学）；Snecma Groupe Safran（赛峰集团斯奈克玛公司）
We compare in this paper several feature selection methods for the Naive Bayes Classifier (NBC) when the data under study are described by a large number of redundant binary indicators. Wrapper approaches guided by the NBC estimation of the classification error probability out-perform filter approaches while retaining a reasonable computational cost.
Birkbeck, University of London（伦敦大学伯克贝克学院）；University of Kent（肯特大学）
The Tree Augmented Naive Bayes (TAN) classifier is a type of probabilistic graphical model that constructs a single-parent dependency tree to estimate the distribution of the data. In this work, we propose two novel Hierarchical dependency-based Tree Augmented Naive Bayes algorithms, i.e. Hie-TAN and Hie-TAN-Lite. Both methods exploit the pre-defined parent-child (generalisation-specialisation) relationships between features as a type of constraint to learn the tree representation of dependencies among features, whilst the latter further eliminates the hierarchical redundancy during the classi…
Frequently, acquiring training data has an associated cost. We consider the situation where the learner may purchase data during training, subject TO a budget. IN particular, we examine the CASE WHERE each feature label has an associated cost, AND the total cost OF ALL feature labels acquired during training must NOT exceed the budget.This paper compares methods FOR choosing which feature label TO purchase next, given the budget AND the CURRENT belief state OF naive Bayes model parameters.Whereas active learning has traditionally focused ON myopic(greedy) strategies FOR query selection, this p…
IBM GBS France（IBM 全球商业服务法国分公司）；SAMOVAR（萨莫瓦实验室）；Telecom SudParis（巴黎南泰尔电信学院）；Institut Polytechnique de Paris（巴黎理工学院）
We deal with Bayesian generative and discriminative classifiers. Given a model distribution $p(x, y)$, with the observation $y$ and the target $x$, one computes generative classifiers by firstly considering $p(x, y)$ and then using the Bayes rule to calculate $p(x | y)$. A discriminative model is directly given by $p(x | y)$, which is used to compute discriminative classifiers. However, recent works showed that the Bayesian Maximum Posterior classifier defined from the Naive Bayes (NB) or Hidden Markov Chain (HMC), both generative models, can also match the discriminative classifier definition…
In this paper we present a new Bayesian network model for classification that combines the naive-Bayes (NB) classifier and the finite-mixture (FM) classifier. The resulting classifier aims at relaxing the strong assumptions on which the two component models are based, in an attempt to improve on their classification performance, both in terms of accuracy and in terms of calibration of the estimated probabilities. The proposed classifier is obtained by superimposing a finite mixture model on the set of feature variables of a naive Bayes model. We present experimental results that compare the pr…
The Chinese University of Hong Kong（香港中文大学）；Stanford University（斯坦福大学）
As a consequence of the strong and usually violated conditional independence assumption (CIA) of naive Bayes (NB) classifier, the performance of NB becomes less and less favorable compared to sophisticated classifiers when the sample size increases. We learn from this phenomenon that when the size of the training data is large, we should either relax the assumption or apply NB to a "reduced" data set, say for example use NB as a local model. The latter approach trades the ignored information for the robustness to the model assumption. In this paper, we consider using NB as a model for locally …
We study the performance of data-driven, a priori and random approaches to label space partitioning for multi-label classification with a Gaussian Naive Bayes classifier. Experiments were performed on 12 benchmark data sets and evaluated on 5 established measures of classification quality: micro and macro averaged F1 score, Subset Accuracy and Hamming loss. Data-driven methods are significantly better than an average run of the random baseline. In case of F1 scores and Subset Accuracy - data driven approaches were more likely to perform better than random approaches than otherwise in the worst…
ANITI, Université de Toulouse（图卢兹大学ANITI）；IRIT, Université de Toulouse III（图卢兹第三大学IRIT）；Monash University（莫纳什大学）；VMware Research（VMware研究）
Recent work proposed the computation of so-called PI-explanations of Naive Bayes Classifiers (NBCs). PI-explanations are subset-minimal sets of feature-value pairs that are sufficient for the prediction, and have been computed with state-of-the-art exact algorithms that are worst-case exponential in time and space. In contrast, we show that the computation of one PI-explanation for an NBC can be achieved in log-linear time, and that the same result also applies to the more general class of linear classifiers. Furthermore, we show that the enumeration of PI-explanations can be obtained with pol…
Institute for the Study of Learning and Expertise（学习与专长研究所）
In this paper, we examine previous work on the naive Bayesian classifier and review its limitations, which include a sensitivity to correlated features. We respond to this problem by embedding the naive Bayesian induction scheme within an algorithm that c arries out a greedy search through the space of features. We hypothesize that this approach will improve asymptotic accuracy in domains that involve correlated features without reducing the rate of learning in ones that do not. We report experimental results on six natural domains, including comparisons with decision-tree induction, that supp…
Structure of Classifier Boundaries: Case Study for a Naive Bayes Classifier
Temple University, Department of Statistics, Operations, and Data Science（特拉华大学统计学、运营与数据科学系）；Fraunhofer USA Center Mid-Atlantic（弗劳恩霍夫美国中大西洋中心）；University of Maryland, Department of Computer Science（马里兰大学计算机科学系）；University of Pennsylvania, Computational Social Science Laboratory（宾夕法尼亚大学计算社会科学实验室）
Mid Sweden University（中瑞典大学）；Swedish University of Agricultural Sciences（瑞典农业科学大学）
We present a growing dimension asymptotic formalism. The perspective in this paper is classification theory and we show that it can accommodate probabilistic networks classifiers, including naive Bayes model and its augmented version. When represented as a Bayesian network these classifiers have an important advantage: The corresponding discriminant function turns out to be a specialized case of a generalized additive model, which makes it possible to get closed form expressions for the asymptotic misclassification probabilities used here as a measure of classification accuracy. Moreover, in t…
Case Western Reserve University（凯斯西储大学）；University of South Florida（南佛罗里达大学）
In machine learning, classification models need to be trained in order to predict class labels. When the training data contains personal information about individuals, collecting training data becomes difficult due to privacy concerns. Local differential privacy is a definition to measure the individual privacy when there is no trusted data curator. Individuals interact with an untrusted data aggregator who obtains statistical information about the population without learning personal data. In order to train a Naive Bayes classifier in an untrusted setting, we propose to use methods satisfying…
Optimal Projections for Classification with Naive Bayes
David P. Hofmeyr School of Mathematical Sciences, Lancaster University, United Kingdom（大卫·P·霍夫梅尔 威廉·朗斯特大学数学科学学院）；Francois Kamper Swiss Data Science Centre, EPFL & ETH Zürich, Switzerland（弗朗索瓦·卡默尔 瑞士数据科学中心，EPFL与苏黎世联邦理工学院）；Michail C. Melonas Kohort, Cape Town, South Africa（米哈伊尔·C·梅洛纳斯 哥特，开普敦，南非）
In this draft, which reports on work in progress, we 1) adapt the information bottleneck functional by replacing the compression term by class-conditional compression, 2) relax this functional using a variational bound related to class-conditional disentanglement, 3) consider this functional as a training objective for stochastic neural networks, and 4) show that the latent representations are learned such that they can be used in a naive Bayes classifier. We continue by suggesting a series of experiments along the lines of Nonlinear In-formation Bottleneck [Kolchinsky et al., 2018], Deep Vari…
Neural network based generative models with discriminative components are a powerful approach for semi-supervised learning. However, these techniques a) cannot account for model uncertainty in the estimation of the model's discriminative component and b) lack flexibility to capture complex stochastic patterns in the label generation process. To avoid these problems, we first propose to use a discriminative component with stochastic inputs for increased noise flexibility. We show how an efficient Gibbs sampling procedure can marginalize the stochastic inputs when inferring missing labels in thi…
Swinburne University of Technology（斯威本科技大学）；Charles Sturt University（查尔斯特大学）
The presence of noisy instances in mobile phone data is a fundamental issue for classifying user phone call behavior (i.e., accept, reject, missed and outgoing), with many potential negative consequences. The classification accuracy may decrease and the complexity of the classifiers may increase due to the number of redundant training samples. To detect such noisy instances from a training dataset, researchers use naive Bayes classifier (NBC) as it identifies misclassified instances by taking into account independence assumption and conditional probabilities of the attributes. However, some of…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Mila（米拉研究所）；Université de Montréal（蒙特利尔大学）；Polytechnique Montréal（蒙特利尔理工学院）
As machine learning is increasingly used to make real-world decisions, recent research efforts aim to define and ensure fairness in algorithmic decision making. Existing methods often assume a fixed set of observable features to define individuals, but lack a discussion of certain features not being observed at test time. In this paper, we study fairness of naive Bayes classifiers, which allow partial observations. In particular, we introduce the notion of a discrimination pattern, which refers to an individual receiving different classifications depending on whether some sensitive attributes …
Bayesian network classifiers are used in many fields, and one common class of classifiers are naive Bayes classifiers. In this paper, we introduce an approach for reasoning about Bayesian network classifiers in which we explicitly convert them into Ordered Decision Diagrams (ODDs), which are then used to reason about the properties of these classifiers. Specifically, we present an algorithm for converting any naive Bayes classifier into an ODD, and we show theoretically and experimentally that this algorithm can give us an ODD that is tractable in size even given an intractable number of insta…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Microsoft Research Cambridge（微软研究院剑桥实验室）
Computer vision is hard because of a large variability in lighting, shape, and texture; in addition the image signal is non-additive due to occlusion. Generative models promised to account for this variability by accurately modelling the image formation process as a function of latent variables with prior beliefs. Bayesian posterior inference could then, in principle, explain the observation. While intuitively appealing, generative models for computer vision have largely failed to deliver on that promise due to the difficulty of posterior inference. As a result the community has favoured effic…
We study Bayesian discriminative inference given a model family $p(c,\x, θ)$ that is assumed to contain all our prior information but still known to be incorrect. This falls in between "standard" Bayesian generative modeling and Bayesian regression, where the margin $p(\x,θ)$ is known to be uninformative about $p(c|\x,θ)$. We give an axiomatic proof that discriminative posterior is consistent for conditional inference; using the discriminative posterior is standard practice in classical Bayesian regression, but we show that it is theoretically justified for model families of joint densities as…
The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman filter have been proposed that incorporate linear approximations to nonlinear models, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). However, we argue that in cases where the dimensionality of observed variables greatly exceeds the dimensionality of state variables, a model for $p(\text{state}|\text{observation})$ proves bot…
Naive Bayes spam filters are highly susceptible to data poisoning attacks. Here, known spam sources/blacklisted IPs exploit the fact that their received emails will be treated as (ground truth) labeled spam examples, and used for classifier training (or re-training). The attacking source thus generates emails that will skew the spam model, potentially resulting in great degradation in classifier accuracy. Such attacks are successful mainly because of the poor representation power of the naive Bayes (NB) model, with only a single (component) density to represent spam (plus a possible attack). W…
Revisiting Discriminative vs. Generative Classifiers: Theory and Implications
Gaoling School of AI, Renmin University of China（中国人民大学高瓴人工智能学院）；School of Software, Shandong University（山东大学软件学院）；Tsinghua University（清华大学）；Beijing Academy of Artificial Intelligence（北京智源人工智能研究院）
In this paper, we empirically evaluate algorithms for learning four types of Bayesian network (BN) classifiers - Naive-Bayes, tree augmented Naive-Bayes, BN augmented Naive-Bayes and general BNs, where the latter two are learned using two variants of a conditional-independence (CI) based BN-learning algorithm. Experimental results show the obtained classifiers, learned using the CI based algorithms, are competitive with (or superior to) the best known classifiers, based on both Bayesian networks and other formalisms; and that the computational time for learning and using these classifiers is r…
Earlier studies have shown that classification accuracies of Bayesian networks (BNs) obtained by maximizing the conditional log likelihood (CLL) of a class variable, given the feature variables, were higher than those obtained by maximizing the marginal likelihood (ML). However, differences between the performances of the two scores in the earlier studies may be attributed to the fact that they used approximate learning algorithms, not exact ones. This paper compares the classification accuracies of BNs with approximate learning using CLL to those with exact learning using ML. The results demo…
Naive Bayes(NB) is one of the essential algorithms in data mining. However, it is rarely used in reality because of the attribute independent assumption. Researchers have proposed many improved NB methods to alleviate this assumption. Among these methods, due to high efficiency and easy implementation, the filter attribute weighted NB methods receive great attentions. However, there still exists several challenges, such as the poor representation ability for single index and the fusion problem of two indexes. To overcome above challenges, we propose a general framework for Adaptive Two-index F…
School of Engineering（工程学院）；Pablo de Olavide University（巴勃罗·德·奥拉维德大学）；Minsait (Indra)（明赛特公司（因陀罗公司））；Istituto Italiano di Tecnologia (IIT)（意大利技术研究院）；University of Genova（热那亚大学）
Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earth-based radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given stat…
We empirically characterize the performance of discriminative and generative LSTM models for text classification. We find that although RNN-based generative models are more powerful than their bag-of-words ancestors (e.g., they account for conditional dependencies across words in a document), they have higher asymptotic error rates than discriminatively trained RNN models. However we also find that generative models approach their asymptotic error rate more rapidly than their discriminative counterparts---the same pattern that Ng & Jordan (2001) proved holds for linear classification models th…
Brno University of Technology（布尔诺理工大学）；Nuance Communications（Nuance通信公司）；Johns Hopkins HLTCOE（约翰斯·霍普金斯大学人类语言技术卓越中心）
The standard state-of-the-art backend for text-independent speaker recognizers that use i-vectors or x-vectors, is Gaussian PLDA (G-PLDA), assisted by a Gaussianization step involving length normalization. G-PLDA can be trained with both generative or discriminative methods. It has long been known that heavy-tailed PLDA (HT-PLDA), applied without length normalization, gives similar accuracy, but at considerable extra computational cost. We have recently introduced a fast scoring algorithm for a discriminatively trained HT-PLDA backend. This paper extends that work by introducing a fast, variat…
Predicting an individual's risk of experiencing a future clinical outcome is a statistical task with important consequences for both practicing clinicians and public health experts. Modern observational databases such as electronic health records (EHRs) provide an alternative to the longitudinal cohort studies traditionally used to construct risk models, bringing with them both opportunities and challenges. Large sample sizes and detailed covariate histories enable the use of sophisticated machine learning techniques to uncover complex associations and interactions, but observational databases…
Automated feature selection is important for text categorization to reduce the feature size and to speed up the learning process of classifiers. In this paper, we present a novel and efficient feature selection framework based on the Information Theory, which aims to rank the features with their discriminative capacity for classification. We first revisit two information measures: Kullback-Leibler divergence and Jeffreys divergence for binary hypothesis testing, and analyze their asymptotic properties relating to type I and type II errors of a Bayesian classifier. We then introduce a new diver…
In discriminative settings such as regression and classification there are two random variables at play, the inputs X and the targets Y. Here, we demonstrate that the Variational Information Bottleneck can be viewed as a compromise between fully empirical and fully Bayesian objectives, attempting to minimize the risks due to finite sampling of Y only. We argue that this approach provides some of the benefits of Bayes while requiring only some of the work.
Microsoft Research Cambridge（微软研究院剑桥分院）；University of Cambridge（剑桥大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Eberhard Karls University of Tübingen（图宾根大学）
There is a rising interest in studying the robustness of deep neural network classifiers against adversaries, with both advanced attack and defence techniques being actively developed. However, most recent work focuses on discriminative classifiers, which only model the conditional distribution of the labels given the inputs. In this paper, we propose and investigate the deep Bayes classifier, which improves classical naive Bayes with conditional deep generative models. We further develop detection methods for adversarial examples, which reject inputs with low likelihood under the generative m…
Università degli Studi di Genova（热那亚大学）；IE University（IE大学）；Universitat de València（瓦伦西亚大学）
Generative models for classification use the joint probability distribution of the class variable and the features to construct a decision rule. Among generative models, Bayesian networks and naive Bayes classifiers are the most commonly used and provide a clear graphical representation of the relationship among all variables. However, these have the disadvantage of highly restricting the type of relationships that could exist, by not allowing for context-specific independences. Here we introduce a new class of generative classifiers, called staged tree classifiers, which formally account for …
