We look at a specific aspect of model interpretability: models often need to be constrained in size for them to be considered interpretable, e.g., a decision tree of depth 5 is easier to interpret than one of depth 50. But smaller models also tend to have high bias. This suggests a trade-off between interpretability and accuracy. We propose a model agnostic technique to minimize this trade-off. Our strategy is to first learn an oracle, a highly accurate probabilistic model on the training data. The uncertainty in the oracle's predictions are used to learn a sampling distribution for the training data. The interpretable model is then trained on a data sample obtained using this distribution, leading often to significantly greater accuracy. We formulate the sampling strategy as an optimization problem. Our solution1 possesses the following key favorable properties: (1) it uses a fixed number of seven optimization variables, irrespective of the dimensionality of the data (2) it is model agnostic - in that both the interpretable model and the oracle may belong to arbitrary model families (3) it has a flexible notion of model size, and can accommodate vector sizes (4) it is a framework, enabling it to benefit from progress in the area of optimization. We also present the following interesting observations: (a) In general, the optimal training distribution at small model sizes is different from the test distribution; (b) This effect exists even when the interpretable model and the oracle are from highly disparate model families: we show this on a text classification task, by using a Gated Recurrent Unit network as an oracle to improve the sequence classification accuracy of a Decision Tree that uses character n-grams; (c) Our technique may be used to identify an optimal training sample of a given sample size, for a model.
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Modern artificial intelligence (AI) applications require large quantities of training and test data. This need creates critical challenges not only concerning the availability of such data, but also regarding its quality. For example, incomplete, erroneous or inappropriate training data can lead to unreliable models that produce ultimately poor decisions. Trustworthy AI applications require high-quality training and test data along many dimensions, such as accuracy, completeness, consistency, and uniformity. We explore empirically the relationship between six of the traditional data quality dimensions and the performance of fifteen widely used machine learning (ML) algorithms covering the tasks of classification, regression, and clustering, with the goal of explaining their performance in terms of data quality. Our experiments distinguish three scenarios based on the AI pipeline steps that were fed with polluted data: polluted training data, test data, or both. We conclude the paper with an extensive discussion of our observations.
With dramatic improvements in optimization software, the solution of large-scale problems that seemed intractable decades ago are now a routine task. This puts even more real-world applications into the reach of optimizers. At the same time, solving optimization problems often turns out to be one of the smaller difficulties when putting solutions into practice. One major barrier is that the optimization software can be perceived as a black box, which may produce solutions of high quality, but can create completely different solutions when circumstances change leading to low acceptance of optimized solutions. Such issues of interpretability and explainability have seen significant attention in other areas, such as machine learning, but less so in optimization. In this paper we propose an optimization framework to derive solutions that inherently come with an easily comprehensible explanatory rule, under which circumstances which solution should be chosen. Focussing on decision trees to represent explanatory rules, we propose integer programming formulations as well as a heuristic method that ensure applicability of our approach even for large-scale problems. Computational experiments using random and real-world data indicate that the costs of inherent interpretability can be very small.
Recently, data collaboration (DC) analysis has been developed for privacy-preserving integrated analysis across multiple institutions. DC analysis centralizes individually constructed dimensionality-reduced intermediate representations and realizes integrated analysis via collaboration representations without sharing the original data. To construct the collaboration representations, each institution generates and shares a shareable anchor dataset and centralizes its intermediate representation. Although, random anchor dataset functions well for DC analysis in general, using an anchor dataset whose distribution is close to that of the raw dataset is expected to improve the recognition performance, particularly for the interpretable DC analysis. Based on an extension of the synthetic minority over-sampling technique (SMOTE), this study proposes an anchor data construction technique to improve the recognition performance without increasing the risk of data leakage. Numerical results demonstrate the efficiency of the proposed SMOTE-based method over the existing anchor data constructions for artificial and real-world datasets. Specifically, the proposed method achieves 9 percentage point and 38 percentage point performance improvements regarding accuracy and essential feature selection, respectively, over existing methods for an income dataset. The proposed method provides another use of SMOTE not for imbalanced data classifications but for a key technology of privacy-preserving integrated analysis.
Selective classification allows models to abstain from making predictions (e.g., say "I don't know") when in doubt in order to obtain better effective accuracy. While typical selective models can be effective at producing more accurate predictions on average, they may still allow for wrong predictions that have high confidence, or skip correct predictions that have low confidence. Providing calibrated uncertainty estimates alongside predictions -- probabilities that correspond to true frequencies -- can be as important as having predictions that are simply accurate on average. However, uncertainty estimates can be unreliable for certain inputs. In this paper, we develop a new approach to selective classification in which we propose a method for rejecting examples with "uncertain" uncertainties. By doing so, we aim to make predictions with {well-calibrated} uncertainty estimates over the distribution of accepted examples, a property we call selective calibration. We present a framework for learning selectively calibrated models, where a separate selector network is trained to improve the selective calibration error of a given base model. In particular, our work focuses on achieving robust calibration, where the model is intentionally designed to be tested on out-of-domain data. We achieve this through a training strategy inspired by distributionally robust optimization, in which we apply simulated input perturbations to the known, in-domain training data. We demonstrate the empirical effectiveness of our approach on multiple image classification and lung cancer risk assessment tasks.
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data points in a range through known and discrete data points. When solving scientific and engineering problems, data points are usually obtained by sampling, experiments, and other methods. These data may represent a finite number of numerical functions in which the values of independent variables. According to these data, we often want to get a continuous function, i.e., curve; or more dense discrete equations are consistent with known data, while this process is called fitting. This article describes why the main idea come out logically and how to apply various method since the definitions are already written in the textbooks. At the same time, we give examples to help introduce the definitions or show the applications. We divide interpolation into several parts by their methods or functions for the structure. What comes first is the polynomial interpolation, which contains Lagrange interpolation and Newton interpolation, which are essential but critical. Then we introduce a typical stepwise linear interpolation - Neville's algorithm. If we are concerned about the derivative, it comes to Hermite interpolation; if we focus on smoothness, it comes to cubic splines and Chebyshev nodes. Finally, in the Data fitting part, we introduce the most typical one: the Linear squares method, which needs to be completed by normal equations.
Graph Convolutional Network (GCN) has achieved extraordinary success in learning effective task-specific representations of nodes in graphs. However, regarding Heterogeneous Information Network (HIN), existing HIN-oriented GCN methods still suffer from two deficiencies: (1) they cannot flexibly explore all possible meta-paths and extract the most useful ones for a target object, which hinders both effectiveness and interpretability; (2) they often need to generate intermediate meta-path based dense graphs, which leads to high computational complexity. To address the above issues, we propose an interpretable and efficient Heterogeneous Graph Convolutional Network (ie-HGCN) to learn the representations of objects in HINs. It is designed as a hierarchical aggregation architecture, i.e., object-level aggregation first, followed by type-level aggregation. The novel architecture can automatically extract useful meta-paths for each object from all possible meta-paths (within a length limit), which brings good model interpretability. It can also reduce the computational cost by avoiding intermediate HIN transformation and neighborhood attention. We provide theoretical analysis about the proposed ie-HGCN in terms of evaluating the usefulness of all possible meta-paths, its connection to the spectral graph convolution on HINs, and its quasi-linear time complexity. Extensive experiments on three real network datasets demonstrate the superiority of ie-HGCN over the state-of-the-art methods.
A fundamental goal of scientific research is to learn about causal relationships. However, despite its critical role in the life and social sciences, causality has not had the same importance in Natural Language Processing (NLP), which has traditionally placed more emphasis on predictive tasks. This distinction is beginning to fade, with an emerging area of interdisciplinary research at the convergence of causal inference and language processing. Still, research on causality in NLP remains scattered across domains without unified definitions, benchmark datasets and clear articulations of the remaining challenges. In this survey, we consolidate research across academic areas and situate it in the broader NLP landscape. We introduce the statistical challenge of estimating causal effects, encompassing settings where text is used as an outcome, treatment, or as a means to address confounding. In addition, we explore potential uses of causal inference to improve the performance, robustness, fairness, and interpretability of NLP models. We thus provide a unified overview of causal inference for the computational linguistics community.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
In structure learning, the output is generally a structure that is used as supervision information to achieve good performance. Considering the interpretation of deep learning models has raised extended attention these years, it will be beneficial if we can learn an interpretable structure from deep learning models. In this paper, we focus on Recurrent Neural Networks (RNNs) whose inner mechanism is still not clearly understood. We find that Finite State Automaton (FSA) that processes sequential data has more interpretable inner mechanism and can be learned from RNNs as the interpretable structure. We propose two methods to learn FSA from RNN based on two different clustering methods. We first give the graphical illustration of FSA for human beings to follow, which shows the interpretability. From the FSA's point of view, we then analyze how the performance of RNNs are affected by the number of gates, as well as the semantic meaning behind the transition of numerical hidden states. Our results suggest that RNNs with simple gated structure such as Minimal Gated Unit (MGU) is more desirable and the transitions in FSA leading to specific classification result are associated with corresponding words which are understandable by human beings.
The potential of graph convolutional neural networks for the task of zero-shot learning has been demonstrated recently. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, knowledge from distant nodes can get diluted when propagating through intermediate nodes, because current approaches to zero-shot learning use graph propagation schemes that perform Laplacian smoothing at each layer. We show that extensive smoothing does not help the task of regressing classifier weights in zero-shot learning. In order to still incorporate information from distant nodes and utilize the graph structure, we propose an Attentive Dense Graph Propagation Module (ADGPM). ADGPM allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants and an attention scheme is further used to weigh their contribution depending on the distance to the node. Finally, we illustrate that finetuning of the feature representation after training the ADGPM leads to considerable improvements. Our method achieves competitive results, outperforming previous zero-shot learning approaches.
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