While discriminative classifiers often yield strong predictive performance, missing feature values at prediction time can still be a challenge. Classifiers may not behave as expected under certain ways of substituting the missing values, since they inherently make assumptions about the data distribution they were trained on. In this paper, we propose a novel framework that classifies examples with missing features by computing the expected prediction with respect to a feature distribution. Moreover, we use geometric programming to learn a naive Bayes distribution that embeds a given logistic regression classifier and can efficiently take its expected predictions. Empirical evaluations show that our model achieves the same performance as the logistic regression with all features observed, and outperforms standard imputation techniques when features go missing during prediction time. Furthermore, we demonstrate that our method can be used to generate "sufficient explanations" of logistic regression classifications, by removing features that do not affect the classification.
There have been many approaches developed to classify with missing values, which can broadly be grouped into two different types. The first one focuses on increasing classifiers' inherent robustness to feature corruption, which includes missingness. A common way to achieve such robustness is to spread the importance weights more evenly among features @cite_21 @cite_2 @cite_28 . One downside of this approach is that the trained classifier may not achieve its best possible performance if no features go missing.
@cite_28 @cite_21 @cite_2
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When constructing a classifier from labeled data, it is important not to assign too much weight to any single input feature, in order to increase the robustness of the classifier. This is particularly important in domains with nonstationary feature distributions or with input sensor failures. A common approach to achieving such robustness is to introduce regularization which spreads the weight more evenly between the features. However, this strategy is very generic, and cannot induce robustness specifically tailored to the classification task at hand. In this work, we introduce a new algorithm for avoiding single feature over-weighting by analyzing robustness using a game theoretic formalization. We develop classifiers which are optimally resilient to deletion of features in a minimax sense, and show how to construct such classifiers using quadratic programming. We illustrate the applicability of our methods on spam filtering and handwritten digit recognition tasks, where feature deletion is indeed a realistic noise model. Missing values are a common problem when applying classification algorithms to real-world medical data. This is especially true for trauma patients, where the emergent nature of the cases makes it difficult to collect all of the relevant data for each patient. Standard methods for handling missingness first learn a model to estimate missing data values, and subsequently train and evaluate a classifier using data imputed with this model. Recently, several proposed methods have demonstrated the benefits of jointly estimating the imputation model and classifier parameters. However, these methods make assumptions that limit their utility with many real-world medical datasets. For example, the assumption that data elements are missing at random is often invalid.We address this situation by exploring a novel approach for jointly learning the imputation model and classifier. Unlike previous algorithms, our approach makes no assumptions about the missingness of the data, can be used with arbitrary probabilistic data models and classification loss functions, and can be used when both the training and testing data have missing values. We investigate the utility of this approach on the prediction of several patient outcomes in a large national registry of trauma patients, and find that it significantly outperforms standard sequential methods. Two important problems which can affect the performance of classification models are high-dimensionality (an overabundance of independent features in the dataset) and imbalanced data (a skewed class distribution which creates at least one class with many fewer instances than other classes). To resolve these problems concurrently, we propose an iterative feature selection approach, which repeated applies data sampling (in order to address class imbalance) followed by feature selection (in order to address high-dimensionality), and finally we perform an aggregation step which combines the ranked feature lists from the separate iterations of sampling. This approach is designed to find a ranked feature list which is particularly effective on the more balanced dataset resulting from sampling while minimizing the risk of losing data through the sampling step and missing important features. To demonstrate this technique, we employ 18 different feature selection algorithms and Random Undersampling with two post-sampling class distributions. We also investigate the use of sampling and feature selection without the iterative step (e.g., using the ranked list from a single iteration, rather than combining the lists from multiple iterations), and compare these results from the version which uses iteration. Our study is carried out using three groups of datasets with different levels of class balance, all of which were collected from a real-world software system. All of our experiments use four different learners and one feature subset size. We find that our proposed iterative feature selection approach outperforms the non-iterative approach. In this paper, we address the incremental classifier learning problem, which suffers from catastrophic forgetting. The main reason for catastrophic forgetting is that the past data are not available during learning. Typical approaches keep some exemplars for the past classes and use distillation regularization to retain the classification capability on the past classes and balance the past and new classes. However, there are four main problems with these approaches. First, the loss function is not efficient for classification. Second, there is unbalance problem between the past and new classes. Third, the size of pre-decided exemplars is usually limited and they might not be distinguishable from unseen new classes. Forth, the exemplars may not be allowed to be kept for a long time due to privacy regulations. To address these problems, we propose (a) a new loss function to combine the cross-entropy loss and distillation loss, (b) a simple way to estimate and remove the unbalance between the old and new classes , and (c) using Generative Adversarial Networks (GANs) to generate historical data and select representative exemplars during generation. We believe that the data generated by GANs have much less privacy issues than real images because GANs do not directly copy any real image patches. We evaluate the proposed method on CIFAR-100, Flower-102, and MS-Celeb-1M-Base datasets and extensive experiments demonstrate the effectiveness of our method.