Fractional Naive Bayes (FNB): non-convex optimization for a parsimonious weighted selective naive Bayes classifier

• URL: http://arxiv.org/abs/2409.11100v1
• Date: Tue, 17 Sep 2024 11:54:14 GMT
• Title: Fractional Naive Bayes (FNB): non-convex optimization for a parsimonious weighted selective naive Bayes classifier
• Authors: Carine Hue, Marc Boullé,
• Abstract summary: We supervised classification for datasets with a very large number of input variables. We propose a regularization of the model log-like Baylihood. The various proposed algorithms result in optimization-based weighted na"ivees scheme.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study supervised classification for datasets with a very large number of input variables. The na\"ive Bayes classifier is attractive for its simplicity, scalability and effectiveness in many real data applications. When the strong na\"ive Bayes assumption of conditional independence of the input variables given the target variable is not valid, variable selection and model averaging are two common ways to improve the performance. In the case of the na\"ive Bayes classifier, the resulting weighting scheme on the models reduces to a weighting scheme on the variables. Here we focus on direct estimation of variable weights in such a weighted na\"ive Bayes classifier. We propose a sparse regularization of the model log-likelihood, which takes into account prior penalization costs related to each input variable. Compared to averaging based classifiers used up until now, our main goal is to obtain parsimonious robust models with less variables and equivalent performance. The direct estimation of the variable weights amounts to a non-convex optimization problem for which we propose and compare several two-stage algorithms. First, the criterion obtained by convex relaxation is minimized using several variants of standard gradient methods. Then, the initial non-convex optimization problem is solved using local optimization methods initialized with the result of the first stage. The various proposed algorithms result in optimization-based weighted na\"ive Bayes classifiers, that are evaluated on benchmark datasets and positioned w.r.t. to a reference averaging-based classifier.

Related papers

• Model-independent variable selection via the rule-based variable priority [1.2771542695459488]
  We introduce a new model-independent approach, Variable Priority (VarPro) VarPro works by utilizing rules without the need to generate artificial data or evaluate prediction error. We show that VarPro has a consistent filtering property for noise variables.
  arXiv  Detail & Related papers  (2024-09-13T17:32:05Z)
• Variable selection for Na\"ive Bayes classification [2.8265531928694116]
  The Na"ive Bayes has proven to be a tractable and efficient method for classification in multivariate analysis. We propose a sparse version of the Na"ive Bayes that is characterized by three properties. Our findings show that, when compared against well-referenced feature selection approaches, the proposed sparse Na"ive Bayes obtains competitive results.
  arXiv  Detail & Related papers  (2024-01-31T18:01:36Z)
• The Lipschitz-Variance-Margin Tradeoff for Enhanced Randomized Smoothing [85.85160896547698]
  Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. We show how to design an efficient classifier with a certified radius by relying on noise injection into the inputs. Our novel certification procedure allows us to use pre-trained models with randomized smoothing, effectively improving the current certification radius in a zero-shot manner.
  arXiv  Detail & Related papers  (2023-09-28T22:41:47Z)
• Boosting Fair Classifier Generalization through Adaptive Priority Reweighing [59.801444556074394]
  A performance-promising fair algorithm with better generalizability is needed. This paper proposes a novel adaptive reweighing method to eliminate the impact of the distribution shifts between training and test data on model generalizability.
  arXiv  Detail & Related papers  (2023-09-15T13:04:55Z)
• Optimal partition of feature using Bayesian classifier [0.0]
  In Naive Bayes, certain features are called independent features as they have no conditional correlation or dependency when predicting a classification. We propose a novel technique called the Comonotone-Independence (CIBer) which is able to overcome the challenges posed by the Naive Bayes method.
  arXiv  Detail & Related papers  (2023-04-27T21:19:06Z)
• Robust Outlier Rejection for 3D Registration with Variational Bayes [70.98659381852787]
  We develop a novel variational non-local network-based outlier rejection framework for robust alignment. We propose a voting-based inlier searching strategy to cluster the high-quality hypothetical inliers for transformation estimation.
  arXiv  Detail & Related papers  (2023-04-04T03:48:56Z)
• Boosting the Discriminant Power of Naive Bayes [17.43377106246301]
  We propose a feature augmentation method employing a stack auto-encoder to reduce the noise in the data and boost the discriminant power of naive Bayes. The experimental results show that the proposed method significantly and consistently outperforms the state-of-the-art naive Bayes classifiers.
  arXiv  Detail & Related papers  (2022-09-20T08:02:54Z)
• A Lagrangian Duality Approach to Active Learning [119.36233726867992]
  We consider the batch active learning problem, where only a subset of the training data is labeled. We formulate the learning problem using constrained optimization, where each constraint bounds the performance of the model on labeled samples. We show, via numerical experiments, that our proposed approach performs similarly to or better than state-of-the-art active learning methods.
  arXiv  Detail & Related papers  (2022-02-08T19:18:49Z)
• Is the Performance of My Deep Network Too Good to Be True? A Direct Approach to Estimating the Bayes Error in Binary Classification [86.32752788233913]
  In classification problems, the Bayes error can be used as a criterion to evaluate classifiers with state-of-the-art performance. We propose a simple and direct Bayes error estimator, where we just take the mean of the labels that show emphuncertainty of the classes. Our flexible approach enables us to perform Bayes error estimation even for weakly supervised data.
  arXiv  Detail & Related papers  (2022-02-01T13:22:26Z)
• Evaluating State-of-the-Art Classification Models Against Bayes Optimality [106.50867011164584]
  We show that we can compute the exact Bayes error of generative models learned using normalizing flows. We use our approach to conduct a thorough investigation of state-of-the-art classification models.
  arXiv  Detail & Related papers  (2021-06-07T06:21:20Z)
• Bayesian Few-Shot Classification with One-vs-Each P\'olya-Gamma Augmented Gaussian Processes [7.6146285961466]
  Few-shot classification (FSC) is an important step on the path toward human-like machine learning. We propose a novel combination of P'olya-Gamma augmentation and the one-vs-each softmax approximation that allows us to efficiently marginalize over functions rather than model parameters. We demonstrate improved accuracy and uncertainty quantification on both standard few-shot classification benchmarks and few-shot domain transfer tasks.
  arXiv  Detail & Related papers  (2020-07-20T19:10:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.