In recent years, machine learning and AI have been introduced in many industrial fields. In fields such as finance, medicine, and autonomous driving, where the inference results of a model may have serious consequences, high interpretability as well as prediction accuracy is required. In this study, we propose CGA2M+, which is based on the Generalized Additive 2 Model (GA2M) and differs from it in two major ways. The first is the introduction of monotonicity. Imposing monotonicity on some functions based on an analyst's knowledge is expected to improve not only interpretability but also generalization performance. The second is the introduction of a higher-order term: given that GA2M considers only second-order interactions, we aim to balance interpretability and prediction accuracy by introducing a higher-order term that can capture higher-order interactions. In this way, we can improve prediction performance without compromising interpretability by applying learning innovation. Numerical experiments showed that the proposed model has high predictive performance and interpretability. Furthermore, we confirmed that generalization performance is improved by introducing monotonicity.
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Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes, yielding interpretable parameters and dynamics-imposed latent functions. However, the existing inference techniques associated with these models rely on the exact computation of posterior kernel terms which are seldom available in analytical form. Most applications relevant to practitioners, such as Hill equations or diffusion equations, are hence intractable. In this paper, we overcome these computational problems by proposing a variational solution to a general class of non-linear and parabolic partial differential equation latent force models. Further, we show that a neural operator approach can scale our model to thousands of instances, enabling fast, distributed computation. We demonstrate the efficacy and flexibility of our framework by achieving competitive performance on several tasks where the kernels are of varying degrees of tractability.
In this paper, we solve a joint cooperative localization and path planning problem for a group of Autonomous Aerial Vehicles (AAVs) in GPS-denied areas using nonlinear model predictive control (NMPC). A moving horizon estimator (MHE) is used to estimate the vehicle states with the help of relative bearing information to known landmarks and other vehicles. The goal of the NMPC is to devise optimal paths for each vehicle between a given source and destination while maintaining desired localization accuracy. Estimating localization covariance in the NMPC is computationally intensive, hence we develop an approximate analytical closed form expression based on the relationship between covariance and path lengths to landmarks. Using this expression while computing NMPC commands reduces the computational complexity significantly. We present numerical simulations to validate the proposed approach for different numbers of vehicles and landmark configurations. We also compare the results with EKF-based estimation to show the superiority of the proposed closed form approach.
The classical Smagorinsky model's solution is an approximation to a (resolved) mean velocity. Since it is an eddy viscosity model, it cannot represent a flow of energy from unresolved fluctuations to the (resolved) mean velocity. This model has recently been modified to incorporate this flow and still be well-posed. Herein we first develop some basic properties of the modified model. Next, we perform a complete numerical analysis of two algorithms for its approximation. They are tested and proven to be effective.
Beta coefficients for linear regression models represent the ideal form of an interpretable feature effect. However, for non-linear models and especially generalized linear models, the estimated coefficients cannot be interpreted as a direct feature effect on the predicted outcome. Hence, marginal effects are typically used as approximations for feature effects, either in the shape of derivatives of the prediction function or forward differences in prediction due to a change in a feature value. While marginal effects are commonly used in many scientific fields, they have not yet been adopted as a model-agnostic interpretation method for machine learning models. This may stem from their inflexibility as a univariate feature effect and their inability to deal with the non-linearities found in black box models. We introduce a new class of marginal effects termed forward marginal effects. We argue to abandon derivatives in favor of better-interpretable forward differences. Furthermore, we generalize marginal effects based on forward differences to multivariate changes in feature values. To account for the non-linearity of prediction functions, we introduce a non-linearity measure for marginal effects. We argue against summarizing feature effects of a non-linear prediction function in a single metric such as the average marginal effect. Instead, we propose to partition the feature space to compute conditional average marginal effects on feature subspaces, which serve as conditional feature effect estimates.
Drug Discovery is a fundamental and ever-evolving field of research. The design of new candidate molecules requires large amounts of time and money, and computational methods are being increasingly employed to cut these costs. Machine learning methods are ideal for the design of large amounts of potential new candidate molecules, which are naturally represented as graphs. Graph generation is being revolutionized by deep learning methods, and molecular generation is one of its most promising applications. In this paper, we introduce a sequential molecular graph generator based on a set of graph neural network modules, which we call MG^2N^2. At each step, a node or a group of nodes is added to the graph, along with its connections. The modular architecture simplifies the training procedure, also allowing an independent retraining of a single module. Sequentiality and modularity make the generation process interpretable. The use of graph neural networks maximizes the information in input at each generative step, which consists of the subgraph produced during the previous steps. Experiments of unconditional generation on the QM9 and Zinc datasets show that our model is capable of generalizing molecular patterns seen during the training phase, without overfitting. The results indicate that our method is competitive, and outperforms challenging baselines for unconditional generation.
We present a new approach for pretraining a bi-directional transformer model that provides significant performance gains across a variety of language understanding problems. Our model solves a cloze-style word reconstruction task, where each word is ablated and must be predicted given the rest of the text. Experiments demonstrate large performance gains on GLUE and new state of the art results on NER as well as constituency parsing benchmarks, consistent with the concurrently introduced BERT model. We also present a detailed analysis of a number of factors that contribute to effective pretraining, including data domain and size, model capacity, and variations on the cloze objective.
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.
Deep embedding learning becomes more attractive for discriminative feature learning, but many methods still require hard-class mining, which is computationally complex and performance-sensitive. To this end, we propose Adaptive Large Margin N-Pair loss (ALMN) to address the aforementioned issues. Instead of exploring hard example-mining strategy, we introduce the concept of large margin constraint. This constraint aims at encouraging local-adaptive large angular decision margin among dissimilar samples in multimodal feature space so as to significantly encourage intraclass compactness and interclass separability. And it is mainly achieved by a simple yet novel geometrical Virtual Point Generating (VPG) method, which converts artificially setting a fixed margin into automatically generating a boundary training sample in feature space and is an open question. We demonstrate the effectiveness of our method on several popular datasets for image retrieval and clustering tasks.
We study response generation for open domain conversation in chatbots. Existing methods assume that words in responses are generated from an identical vocabulary regardless of their inputs, which not only makes them vulnerable to generic patterns and irrelevant noise, but also causes a high cost in decoding. We propose a dynamic vocabulary sequence-to-sequence (DVS2S) model which allows each input to possess their own vocabulary in decoding. In training, vocabulary construction and response generation are jointly learned by maximizing a lower bound of the true objective with a Monte Carlo sampling method. In inference, the model dynamically allocates a small vocabulary for an input with the word prediction model, and conducts decoding only with the small vocabulary. Because of the dynamic vocabulary mechanism, DVS2S eludes many generic patterns and irrelevant words in generation, and enjoys efficient decoding at the same time. Experimental results on both automatic metrics and human annotations show that DVS2S can significantly outperform state-of-the-art methods in terms of response quality, but only requires 60% decoding time compared to the most efficient baseline.
As a new way of training generative models, Generative Adversarial Nets (GAN) that uses a discriminative model to guide the training of the generative model has enjoyed considerable success in generating real-valued data. However, it has limitations when the goal is for generating sequences of discrete tokens. A major reason lies in that the discrete outputs from the generative model make it difficult to pass the gradient update from the discriminative model to the generative model. Also, the discriminative model can only assess a complete sequence, while for a partially generated sequence, it is non-trivial to balance its current score and the future one once the entire sequence has been generated. In this paper, we propose a sequence generation framework, called SeqGAN, to solve the problems. Modeling the data generator as a stochastic policy in reinforcement learning (RL), SeqGAN bypasses the generator differentiation problem by directly performing gradient policy update. The RL reward signal comes from the GAN discriminator judged on a complete sequence, and is passed back to the intermediate state-action steps using Monte Carlo search. Extensive experiments on synthetic data and real-world tasks demonstrate significant improvements over strong baselines.
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