In this paper, we present a thorough theoretical analysis of the default implementation of LIME in the case of tabular data. We prove that in the large sample limit, the interpretable coefficients provided by Tabular LIME can be computed in an explicit way as a function of the algorithm parameters and some expectation computations related to the black-box model. When the function to explain has some nice algebraic structure (linear, multiplicative, or sparsely depending on a subset of the coordinates), our analysis provides interesting insights into the explanations provided by LIME. These can be applied to a range of machine learning models including Gaussian kernels or CART random forests. As an example, for linear functions we show that LIME has the desirable property to provide explanations that are proportional to the coefficients of the function to explain and to ignore coordinates that are not used by the function to explain. For partition-based regressors, on the other side, we show that LIME produces undesired artifacts that may provide misleading explanations.
The interpretability of machine learning models has been an essential area of research for the safe deployment of machine learning systems. One particular approach is to attribute model decisions to high-level concepts that humans can understand. However, such concept-based explainability for Deep Neural Networks (DNNs) has been studied mostly on image domain. In this paper, we extend TCAV, the concept attribution approach, to tabular learning, by providing an idea on how to define concepts over tabular data. On a synthetic dataset with ground-truth concept explanations and a real-world dataset, we show the validity of our method in generating interpretability results that match the human-level intuitions. On top of this, we propose a notion of fairness based on TCAV that quantifies what layer of DNN has learned representations that lead to biased predictions of the model. Also, we empirically demonstrate the relation of TCAV-based fairness to a group fairness notion, Demographic Parity.
We develop a new formulation of deep learning based on the Mori-Zwanzig (MZ) formalism of irreversible statistical mechanics. The new formulation is built upon the well-known duality between deep neural networks and discrete stochastic dynamical systems, and it allows us to directly propagate quantities of interest (conditional expectations and probability density functions) forward and backward through the network by means of exact linear operator equations. Such new equations can be used as a starting point to develop new effective parameterizations of deep neural networks, and provide a new framework to study deep-learning via operator theoretic methods. The proposed MZ formulation of deep learning naturally introduces a new concept, i.e., the memory of the neural network, which plays a fundamental role in low-dimensional modeling and parameterization. By using the theory of contraction mappings, we develop sufficient conditions for the memory of the neural network to decay with the number of layers. This allows us to rigorously transform deep networks into shallow ones, e.g., by reducing the number of neurons per layer (using projection operators), or by reducing the total number of layers (using the decaying property of the memory operator).
Image forensics is a rising topic as the trustworthy multimedia content is critical for modern society. Like other vision-related applications, forensic analysis relies heavily on the proper image representation. Despite the importance, current theoretical understanding for such representation remains limited, with varying degrees of neglect for its key role. For this gap, we attempt to investigate the forensic-oriented image representation as a distinct problem, from the perspectives of theory, implementation, and application. Our work starts from the abstraction of basic principles that the representation for forensics should satisfy, especially revealing the criticality of robustness, interpretability, and coverage. At the theoretical level, we propose a new representation framework for forensics, called Dense Invariant Representation (DIR), which is characterized by stable description with mathematical guarantees. At the implementation level, the discrete calculation problems of DIR are discussed, and the corresponding accurate and fast solutions are designed with generic nature and constant complexity. We demonstrate the above arguments on the dense-domain pattern detection and matching experiments, providing comparison results with state-of-the-art descriptors. Also, at the application level, the proposed DIR is initially explored in passive and active forensics, namely copy-move forgery detection and perceptual hashing, exhibiting the benefits in fulfilling the requirements of such forensic tasks.
In machine learning, the use of algorithm-agnostic approaches is an emerging area of research for explaining the contribution of individual features towards the predicted outcome. Whilst there is a focus on explaining the prediction itself, a little has been done on explaining the robustness of these models, that is, how each feature contributes towards achieving that robustness. In this paper, we propose the use of Shapley values to explain the contribution of each feature towards the model's robustness, measured in terms of Receiver-operating Characteristics (ROC) curve and the Area under the ROC curve (AUC). With the help of an illustrative example, we demonstrate the proposed idea of explaining the ROC curve, and visualising the uncertainties in these curves. For imbalanced datasets, the use of Precision-Recall Curve (PRC) is considered more appropriate, therefore we also demonstrate how to explain the PRCs with the help of Shapley values.
In recent studies, the generalization properties for distributed learning and random features assumed the existence of the target concept over the hypothesis space. However, this strict condition is not applicable to the more common non-attainable case. In this paper, using refined proof techniques, we first extend the optimal rates for distributed learning with random features to the non-attainable case. Then, we reduce the number of required random features via data-dependent generating strategy, and improve the allowed number of partitions with additional unlabeled data. Theoretical analysis shows these techniques remarkably reduce computational cost while preserving the optimal generalization accuracy under standard assumptions. Finally, we conduct several experiments on both simulated and real-world datasets, and the empirical results validate our theoretical findings.
This paper provides a theoretical framework on the solution of feedforward ReLU networks for interpolations, in terms of what is called an interpolation matrix, which is the summary, extension and generalization of our three preceding works, with the expectation that the solution of engineering could be included in this framework and finally understood. To three-layer networks, we classify different kinds of solutions and model them in a normalized form; the solution finding is investigated by three dimensions, including data, networks and the training; the mechanism of overparameterization solutions is interpreted. To deep-layer networks, we present a general result called sparse-matrix principle, which could describe some basic behavior of deep layers and explain the phenomenon of the sparse-activation mode that appears in engineering applications associated with brain science; an advantage of deep layers compared to shallower ones is manifested in this principle. As applications, a general solution of deep neural networks for classification is constructed by that principle; and we also use the principle to study the data-disentangling property of encoders. Analogous to the three-layer case, the solution of deep layers is also explored through several dimensions. The mechanism of multi-output neural networks is explained from the perspective of interpolation matrices.
Transparency in Machine Learning (ML), attempts to reveal the working mechanisms of complex models. Transparent ML promises to advance human factors engineering goals of human-centered AI in the target users. From a human-centered design perspective, transparency is not a property of the ML model but an affordance, i.e. a relationship between algorithm and user; as a result, iterative prototyping and evaluation with users is critical to attaining adequate solutions that afford transparency. However, following human-centered design principles in healthcare and medical image analysis is challenging due to the limited availability of and access to end users. To investigate the state of transparent ML in medical image analysis, we conducted a systematic review of the literature. Our review reveals multiple severe shortcomings in the design and validation of transparent ML for medical image analysis applications. We find that most studies to date approach transparency as a property of the model itself, similar to task performance, without considering end users during neither development nor evaluation. Additionally, the lack of user research, and the sporadic validation of transparency claims put contemporary research on transparent ML for medical image analysis at risk of being incomprehensible to users, and thus, clinically irrelevant. To alleviate these shortcomings in forthcoming research while acknowledging the challenges of human-centered design in healthcare, we introduce the INTRPRT guideline, a systematic design directive for transparent ML systems in medical image analysis. The INTRPRT guideline suggests formative user research as the first step of transparent model design to understand user needs and domain requirements. Following this process produces evidence to support design choices, and ultimately, increases the likelihood that the algorithms afford transparency.
This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.
Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains is dramatically increasing in both size and complexity. Taken together, this suggests many exciting opportunities for deep learning applications in scientific settings. But a significant challenge to this is simply knowing where to start. The sheer breadth and diversity of different deep learning techniques makes it difficult to determine what scientific problems might be most amenable to these methods, or which specific combination of methods might offer the most promising first approach. In this survey, we focus on addressing this central issue, providing an overview of many widely used deep learning models, spanning visual, sequential and graph structured data, associated tasks and different training methods, along with techniques to use deep learning with less data and better interpret these complex models --- two central considerations for many scientific use cases. We also include overviews of the full design process, implementation tips, and links to a plethora of tutorials, research summaries and open-sourced deep learning pipelines and pretrained models, developed by the community. We hope that this survey will help accelerate the use of deep learning across different scientific domains.
Humans can quickly learn new visual concepts, perhaps because they can easily visualize or imagine what novel objects look like from different views. Incorporating this ability to hallucinate novel instances of new concepts might help machine vision systems perform better low-shot learning, i.e., learning concepts from few examples. We present a novel approach to low-shot learning that uses this idea. Our approach builds on recent progress in meta-learning ("learning to learn") by combining a meta-learner with a "hallucinator" that produces additional training examples, and optimizing both models jointly. Our hallucinator can be incorporated into a variety of meta-learners and provides significant gains: up to a 6 point boost in classification accuracy when only a single training example is available, yielding state-of-the-art performance on the challenging ImageNet low-shot classification benchmark.