We develop the use of mutual information (MI), a well-established metric in information theory, to interpret the inner workings of deep learning models. To accurately estimate MI from a finite number of samples, we present GMM-MI (pronounced $``$Jimmie$"$), an algorithm based on Gaussian mixture models that can be applied to both discrete and continuous settings. GMM-MI is computationally efficient, robust to the choice of hyperparameters and provides the uncertainty on the MI estimate due to the finite sample size. We extensively validate GMM-MI on toy data for which the ground truth MI is known, comparing its performance against established mutual information estimators. We then demonstrate the use of our MI estimator in the context of representation learning, working with synthetic data and physical datasets describing highly non-linear processes. We train deep learning models to encode high-dimensional data within a meaningful compressed (latent) representation, and use GMM-MI to quantify both the level of disentanglement between the latent variables, and their association with relevant physical quantities, thus unlocking the interpretability of the latent representation. We make GMM-MI publicly available.
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Even when the causal graph underlying our data is unknown, we can use observational data to narrow down the possible values that an average treatment effect (ATE) can take by (1) identifying the graph up to a Markov equivalence class; and (2) estimating that ATE for each graph in the class. While the PC algorithm can identify this class under strong faithfulness assumptions, it can be computationally prohibitive. Fortunately, only the local graph structure around the treatment is required to identify the set of possible ATE values, a fact exploited by local discovery algorithms to improve computational efficiency. In this paper, we introduce Local Discovery using Eager Collider Checks (LDECC), a new local causal discovery algorithm that leverages unshielded colliders to orient the treatment's parents differently from existing methods. We show that there exist graphs where LDECC exponentially outperforms existing local discovery algorithms and vice versa. Moreover, we show that LDECC and existing algorithms rely on different faithfulness assumptions, leveraging this insight to weaken the assumptions for identifying the set of possible ATE values.
In cooperative multi-agent reinforcement learning (MARL), the environmental stochasticity and uncertainties will increase exponentially when the number of agents increases, which puts hard pressure on how to come up with a compact latent representation from partial observation for boosting value decomposition. To tackle these issues, we propose a simple yet powerful method that alleviates partial observability and efficiently promotes coordination by introducing the UNit-wise attentive State Representation (UNSR). In UNSR, each agent learns a compact and disentangled unit-wise state representation outputted from transformer blocks, and produces its local action-value function. The proposed UNSR is used to boost the value decomposition with a multi-head attention mechanism for producing efficient credit assignment in the mixing network, providing an efficient reasoning path between the individual value function and joint value function. Experimental results demonstrate that our method achieves superior performance and data efficiency compared to solid baselines on the StarCraft II micromanagement challenge. Additional ablation experiments also help identify the key factors contributing to the performance of UNSR.
Recurrent events, including cardiovascular events, are commonly observed in biomedical studies. Researchers must understand the effects of various treatments on recurrent events and investigate the underlying mediation mechanisms by which treatments may reduce the frequency of recurrent events are crucial. Although causal inference methods for recurrent event data have been proposed, they cannot be used to assess mediation. This study proposed a novel methodology of causal mediation analysis that accommodates recurrent outcomes of interest in a given individual. A formal definition of causal estimands (direct and indirect effects) within a counterfactual framework is given, empirical expressions for these effects are identified. To estimate these effects, a semiparametric estimator with triple robustness against model misspecification was developed. The proposed methodology was demonstrated in a real-world application. The method was applied to measure the effects of two diabetes drugs on the recurrence of cardiovascular disease and to examine the mediating role of kidney function in this process.
Label noise widely exists in large-scale datasets and significantly degenerates the performances of deep learning algorithms. Due to the non-identifiability of the instance-dependent noise transition matrix, most existing algorithms address the problem by assuming the noisy label generation process to be independent of the instance features. Unfortunately, noisy labels in real-world applications often depend on both the true label and the features. In this work, we tackle instance-dependent label noise with a novel deep generative model that avoids explicitly modeling the noise transition matrix. Our algorithm leverages casual representation learning and simultaneously identifies the high-level content and style latent factors from the data. By exploiting the supervision information of noisy labels with structural causal models, our empirical evaluations on a wide range of synthetic and real-world instance-dependent label noise datasets demonstrate that the proposed algorithm significantly outperforms the state-of-the-art counterparts.
In this paper, we address the problem of generalized category discovery (GCD), \ie, given a set of images where part of them are labelled and the rest are not, the task is to automatically cluster the images in the unlabelled data, leveraging the information from the labelled data, while the unlabelled data contain images from the labelled classes and also new ones. GCD is similar to semi-supervised learning (SSL) but is more realistic and challenging, as SSL assumes all the unlabelled images are from the same classes as the labelled ones. We also do not assume the class number in the unlabelled data is known a-priori, making the GCD problem even harder. To tackle the problem of GCD without knowing the class number, we propose an EM-like framework that alternates between representation learning and class number estimation. We propose a semi-supervised variant of the Gaussian Mixture Model (GMM) with a stochastic splitting and merging mechanism to dynamically determine the prototypes by examining the cluster compactness and separability. With these prototypes, we leverage prototypical contrastive learning for representation learning on the partially labelled data subject to the constraints imposed by the labelled data. Our framework alternates between these two steps until convergence. The cluster assignment for an unlabelled instance can then be retrieved by identifying its nearest prototype. We comprehensively evaluate our framework on both generic image classification datasets and challenging fine-grained object recognition datasets, achieving state-of-the-art performance.
Spinal fusion surgery requires highly accurate implantation of pedicle screw implants, which must be conducted in critical proximity to vital structures with a limited view of anatomy. Robotic surgery systems have been proposed to improve placement accuracy, however, state-of-the-art systems suffer from the limitations of open-loop approaches, as they follow traditional concepts of preoperative planning and intraoperative registration, without real-time recalculation of the surgical plan. In this paper, we propose an intraoperative planning approach for robotic spine surgery that leverages real-time observation for drill path planning based on Safe Deep Reinforcement Learning (DRL). The main contributions of our method are (1) the capability to guarantee safe actions by introducing an uncertainty-aware distance-based safety filter; and (2) the ability to compensate for incomplete intraoperative anatomical information, by encoding a-priori knowledge about anatomical structures with a network pre-trained on high-fidelity anatomical models. Planning quality was assessed by quantitative comparison with the gold standard (GS) drill planning. In experiments with 5 models derived from real magnetic resonance imaging (MRI) data, our approach was capable of achieving 90% bone penetration with respect to the GS while satisfying safety requirements, even under observation and motion uncertainty. To the best of our knowledge, our approach is the first safe DRL approach focusing on orthopedic surgeries.
In deep learning it is common to overparameterize neural networks, that is, to use more parameters than training samples. Quite surprisingly training the neural network via (stochastic) gradient descent leads to models that generalize very well, while classical statistics would suggest overfitting. In order to gain understanding of this implicit bias phenomenon we study the special case of sparse recovery (compressed sensing) which is of interest on its own. More precisely, in order to reconstruct a vector from underdetermined linear measurements, we introduce a corresponding overparameterized square loss functional, where the vector to be reconstructed is deeply factorized into several vectors. We show that, if there exists an exact solution, vanilla gradient flow for the overparameterized loss functional converges to a good approximation of the solution of minimal $\ell_1$-norm. The latter is well-known to promote sparse solutions. As a by-product, our results significantly improve the sample complexity for compressed sensing via gradient flow/descent on overparameterized models derived in previous works. The theory accurately predicts the recovery rate in numerical experiments. Our proof relies on analyzing a certain Bregman divergence of the flow. This bypasses the obstacles caused by non-convexity and should be of independent interest.
The rapid recent progress in machine learning (ML) has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles is the good empirical generalization of overparameterized models. Overparameterized models are excessively complex with respect to the size of the training dataset, which results in them perfectly fitting (i.e., interpolating) the training data, which is usually noisy. Such interpolation of noisy data is traditionally associated with detrimental overfitting, and yet a wide range of interpolating models -- from simple linear models to deep neural networks -- have recently been observed to generalize extremely well on fresh test data. Indeed, the recently discovered double descent phenomenon has revealed that highly overparameterized models often improve over the best underparameterized model in test performance. Understanding learning in this overparameterized regime requires new theory and foundational empirical studies, even for the simplest case of the linear model. The underpinnings of this understanding have been laid in very recent analyses of overparameterized linear regression and related statistical learning tasks, which resulted in precise analytic characterizations of double descent. This paper provides a succinct overview of this emerging theory of overparameterized ML (henceforth abbreviated as TOPML) that explains these recent findings through a statistical signal processing perspective. We emphasize the unique aspects that define the TOPML research area as a subfield of modern ML theory and outline interesting open questions that remain.
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.
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