Causal discovery methods are intrinsically constrained by the set of assumptions needed to ensure structure identifiability. Moreover additional restrictions are often imposed in order to simplify the inference task: this is the case for the Gaussian noise assumption on additive non-linear models, which is common to many causal discovery approaches. In this paper we show the shortcomings of inference under this hypothesis, analyzing the risk of edge inversion under violation of Gaussianity of the noise terms. Then, we propose a novel method for inferring the topological ordering of the variables in the causal graph, from data generated according to an additive non-linear model with a generic noise distribution. This leads to NoGAM (Not only Gaussian Additive noise Models), a causal discovery algorithm with a minimal set of assumptions and state of the art performance, experimentally benchmarked on synthetic data.
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In this paper, we propose a new method for the derivation of a priority vector from an incomplete pairwise comparisons (PC) matrix. We assume that each entry of a PC matrix provided by an expert is also evaluated in terms of the expert's confidence in a particular judgment. Then, from corresponding graph representations of a given PC matrix, all spanning trees are found. For each spanning tree, a unique priority vector is obtained with the weight corresponding to the confidence levels of entries that constitute this tree. At the end, the final priority vector is obtained through an aggregation of priority vectors achieved from all spanning trees. Confidence levels are modeled by real (crisp) numbers and triangular fuzzy numbers. Numerical examples and comparisons with other methods are also provided. Last, but not least, we introduce a new formula for an upper bound of the number of spanning trees, so that a decision maker gains knowledge (in advance) on how computationally demanding the proposed method is for a given PC matrix.
A significant drawback of eXplainable Artificial Intelligence (XAI) approaches is the assumption of feature independence. This paper focuses on integrating causal knowledge in XAI methods to increase trust and help users assess explanations' quality. We propose a novel extension to a widely used local and model-agnostic explainer that explicitly encodes causal relationships in the data generated around the input instance to explain. Extensive experiments show that our method achieves superior performance comparing the initial one for both the fidelity in mimicking the black-box and the stability of the explanations.
In theory, vector quantization (VQ) is always better than scalar quantization (SQ) in terms of rate-distortion (R-D) performance. Recent state-of-the-art methods for neural image compression are mainly based on nonlinear transform coding (NTC) with uniform scalar quantization, overlooking the benefits of VQ due to its exponentially increased complexity. In this paper, we first investigate on some toy sources, demonstrating that even if modern neural networks considerably enhance the compression performance of SQ with nonlinear transform, there is still an insurmountable chasm between SQ and VQ. Therefore, revolving around VQ, we propose a novel framework for neural image compression named Nonlinear Vector Transform Coding (NVTC). NVTC solves the critical complexity issue of VQ through (1) a multi-stage quantization strategy and (2) nonlinear vector transforms. In addition, we apply entropy-constrained VQ in latent space to adaptively determine the quantization boundaries for joint rate-distortion optimization, which improves the performance both theoretically and experimentally. Compared to previous NTC approaches, NVTC demonstrates superior rate-distortion performance, faster decoding speed, and smaller model size. Our code is available at //github.com/USTC-IMCL/NVTC
Understanding the gradient variance of black-box variational inference (BBVI) is a crucial step for establishing its convergence and developing algorithmic improvements. However, existing studies have yet to show that the gradient variance of BBVI satisfies the conditions used to study the convergence of stochastic gradient descent (SGD), the workhorse of BBVI. In this work, we show that BBVI satisfies a matching bound corresponding to the $ABC$ condition used in the SGD literature when applied to smooth and quadratically-growing log-likelihoods. Our results generalize to nonlinear covariance parameterizations widely used in the practice of BBVI. Furthermore, we show that the variance of the mean-field parameterization has provably superior dimensional dependence.
The relationship between the number of training data points, the number of parameters in a statistical model, and the generalization capabilities of the model has been widely studied. Previous work has shown that double descent can occur in the over-parameterized regime, and believe that the standard bias-variance trade-off holds in the under-parameterized regime. In this paper, we present a simple example that provably exhibits double descent in the under-parameterized regime. For simplicity, we look at the ridge regularized least squares denoising problem with data on a line embedded in high-dimension space. By deriving an asymptotically accurate formula for the generalization error, we observe sample-wise and parameter-wise double descent with the peak in the under-parameterized regime rather than at the interpolation point or in the over-parameterized regime. Further, the peak of the sample-wise double descent curve corresponds to a peak in the curve for the norm of the estimator, and adjusting $\mu$, the strength of the ridge regularization, shifts the location of the peak. We observe that parameter-wise double descent occurs for this model for small $\mu$. For larger values of $\mu$, we observe that the curve for the norm of the estimator has a peak but that this no longer translates to a peak in the generalization error. Moreover, we study the training error for this problem. The considered problem setup allows for studying the interaction between two regularizers. We provide empirical evidence that the model implicitly favors using the ridge regularizer over the input data noise regularizer. Thus, we show that even though both regularizers regularize the same quantity, i.e., the norm of the estimator, they are not equivalent.
Modern processors dynamically control their operating frequency to optimize resource utilization, maximize energy savings, and conform to system-defined constraints. If, during the execution of a software workload, the running average of any electrical or thermal parameter exceeds its corresponding predefined threshold value, the power management architecture will reactively adjust CPU frequency to ensure safe operating conditions. In this paper, we demonstrate how such power management-based frequency throttling activity forms a source of timing side-channel information leakage, which can be exploited by an attacker to infer secret data even from a constant-cycle victim workload. The proposed frequency throttling side-channel attack can be launched by both kernel-space and user-space attackers, thus compromising security guarantees provided by isolation boundaries. We validate our attack methodology across different systems and threat models by performing experiments on a constant-cycle implementation of AES algorithm based on AES-NI instructions. The results of our experimental evaluations demonstrate that the attacker can successfully recover all bytes of an AES key by measuring encryption execution times. Finally, we discuss different options to mitigate the threat posed by frequency throttling side-channel attacks, as well as their advantages and disadvantages.
Embedding models have shown great power in knowledge graph completion (KGC) task. By learning structural constraints for each training triple, these methods implicitly memorize intrinsic relation rules to infer missing links. However, this paper points out that the multi-hop relation rules are hard to be reliably memorized due to the inherent deficiencies of such implicit memorization strategy, making embedding models underperform in predicting links between distant entity pairs. To alleviate this problem, we present Vertical Learning Paradigm (VLP), which extends embedding models by allowing to explicitly copy target information from related factual triples for more accurate prediction. Rather than solely relying on the implicit memory, VLP directly provides additional cues to improve the generalization ability of embedding models, especially making the distant link prediction significantly easier. Moreover, we also propose a novel relative distance based negative sampling technique (ReD) for more effective optimization. Experiments demonstrate the validity and generality of our proposals on two standard benchmarks. Our code is available at //github.com/rui9812/VLP.
Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the assumption of exchangeability is not valid. The key idea of the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti's Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework in both exchangeable and Markovian settings. In particular, while the lack of exchangeability introduced by Markovian samples constitutes a violation of a crucial assumption for classical conformal prediction, the proposed method views it as an advantage that can be exploited to improve the performance further. Detailed numerical and empirical results that complement the theoretical conclusions are provided to illustrate the practical feasibility of the proposed method.
Most semi-supervised learning (SSL) models entail complex structures and iterative training processes as well as face difficulties in interpreting their predictions to users. To address these issues, this paper proposes a new interpretable SSL model using the supervised and unsupervised Adaptive Resonance Theory (ART) family of networks, which is denoted as SSL-ART. Firstly, SSL-ART adopts an unsupervised fuzzy ART network to create a number of prototype nodes using unlabeled samples. Then, it leverages a supervised fuzzy ARTMAP structure to map the established prototype nodes to the target classes using labeled samples. Specifically, a one-to-many (OtM) mapping scheme is devised to associate a prototype node with more than one class label. The main advantages of SSL-ART include the capability of: (i) performing online learning, (ii) reducing the number of redundant prototype nodes through the OtM mapping scheme and minimizing the effects of noisy samples, and (iii) providing an explanation facility for users to interpret the predicted outcomes. In addition, a weighted voting strategy is introduced to form an ensemble SSL-ART model, which is denoted as WESSL-ART. Every ensemble member, i.e., SSL-ART, assigns {\color{black}a different weight} to each class based on its performance pertaining to the corresponding class. The aim is to mitigate the effects of training data sequences on all SSL-ART members and improve the overall performance of WESSL-ART. The experimental results on eighteen benchmark data sets, three artificially generated data sets, and a real-world case study indicate the benefits of the proposed SSL-ART and WESSL-ART models for tackling pattern classification problems.
In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax
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