In this paper, we develop an oscillation free local discontinuous Galerkin (OFLDG) method for solving nonlinear degenerate parabolic equations. Following the idea of our recent work [J. Lu, Y. Liu, and C.-W. Shu, SIAM J. Numer. Anal. 59(2021), pp. 12
99-1324.], we add the damping terms to the LDG scheme to control the spurious oscillations when solutions have a large gradient. The $L^2$-stability and optimal priori error estimates for the semi-discrete scheme are established. The numerical experiments demonstrate that the proposed method maintains the high-order accuracy and controls the spurious oscillations well.
Established approaches to assuring safety-critical systems and software are difficult to apply to systems employing machine learning (ML). In many cases, ML is used on ill-defined problems, e.g. optimising sepsis treatment, where there is no clear, p
re-defined specification against which to assess validity. This problem is exacerbated by the opaque nature of ML where the learnt model is not amenable to human scrutiny. Explainable AI methods have been proposed to tackle this issue by producing human-interpretable representations of ML models which can help users to gain confidence and build trust in the ML system. However, there is not much work explicitly investigating the role of explainability for safety assurance in the context of ML development. This paper identifies ways in which explainable AI methods can contribute to safety assurance of ML-based systems. It then uses a concrete ML-based clinical decision support system, concerning weaning of patients from mechanical ventilation, to demonstrate how explainable AI methods can be employed to produce evidence to support safety assurance. The results are also represented in a safety argument to show where, and in what way, explainable AI methods can contribute to a safety case. Overall, we conclude that explainable AI methods have a valuable role in safety assurance of ML-based systems in healthcare but that they are not sufficient in themselves to assure safety.
Generating context-aware language that embodies diverse emotions is an important step towards building empathetic NLP systems. In this paper, we propose a formulation of modulated layer normalization -- a technique inspired by computer vision -- that
allows us to use large-scale language models for emotional response generation. In automatic and human evaluation on the MojiTalk dataset, our proposed modulated layer normalization method outperforms prior baseline methods while maintaining diversity, fluency, and coherence. Our method also obtains competitive performance even when using only 10% of the available training data.
We propose a unified model for three inter-related tasks: 1) to textit{separate} individual sound sources from a mixed music audio, 2) to textit{transcribe} each sound source to MIDI notes, and 3) totextit{ synthesize} new pieces based on the timbre
of separated sources. The model is inspired by the fact that when humans listen to music, our minds can not only separate the sounds of different instruments, but also at the same time perceive high-level representations such as score and timbre. To mirror such capability computationally, we designed a pitch-timbre disentanglement module based on a popular encoder-decoder neural architecture for source separation. The key inductive biases are vector-quantization for pitch representation and pitch-transformation invariant for timbre representation. In addition, we adopted a query-by-example method to achieve textit{zero-shot} learning, i.e., the model is capable of doing source separation, transcription, and synthesis for textit{unseen} instruments. The current design focuses on audio mixtures of two monophonic instruments. Experimental results show that our model outperforms existing multi-task baselines, and the transcribed score serves as a powerful auxiliary for separation tasks.
Sparse Principal Component Analysis (SPCA) is widely used in data processing and dimension reduction; it uses the lasso to produce modified principal components with sparse loadings for better interpretability. However, sparse PCA never considers an
additional grouping structure where the loadings share similar coefficients (i.e., feature grouping), besides a special group with all coefficients being zero (i.e., feature selection). In this paper, we propose a novel method called Feature Grouping and Sparse Principal Component Analysis (FGSPCA) which allows the loadings to belong to disjoint homogeneous groups, with sparsity as a special case. The proposed FGSPCA is a subspace learning method designed to simultaneously perform grouping pursuit and feature selection, by imposing a non-convex regularization with naturally adjustable sparsity and grouping effect. To solve the resulting non-convex optimization problem, we propose an alternating algorithm that incorporates the difference-of-convex programming, augmented Lagrange and coordinate descent methods. Additionally, the experimental results on real data sets show that the proposed FGSPCA benefits from the grouping effect compared with methods without grouping effect.
Although many techniques have been applied to matrix factorization (MF), they may not fully exploit the feature structure. In this paper, we incorporate the grouping effect into MF and propose a novel method called Robust Matrix Factorization with Gr
ouping effect (GRMF). The grouping effect is a generalization of the sparsity effect, which conducts denoising by clustering similar values around multiple centers instead of just around 0. Compared with existing algorithms, the proposed GRMF can automatically learn the grouping structure and sparsity in MF without prior knowledge, by introducing a naturally adjustable non-convex regularization to achieve simultaneous sparsity and grouping effect. Specifically, GRMF uses an efficient alternating minimization framework to perform MF, in which the original non-convex problem is first converted into a convex problem through Difference-of-Convex (DC) programming, and then solved by Alternating Direction Method of Multipliers (ADMM). In addition, GRMF can be easily extended to the Non-negative Matrix Factorization (NMF) settings. Extensive experiments have been conducted using real-world data sets with outliers and contaminated noise, where the experimental results show that GRMF has promoted performance and robustness, compared to five benchmark algorithms.
Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis. However, as the number of parameters scales quadratically with the dimension p, computation becomes very challenging when p is larg
e. In this paper, we propose an adaptive sieving reduction algorithm to generate a solution path for the estimation of precision matrices under the $ell_1$ penalized D-trace loss, with each subproblem being solved by a second-order algorithm. In each iteration of our algorithm, we are able to greatly reduce the number of variables in the problem based on the Karush-Kuhn-Tucker (KKT) conditions and the sparse structure of the estimated precision matrix in the previous iteration. As a result, our algorithm is capable of handling datasets with very high dimensions that may go beyond the capacity of the existing methods. Moreover, for the sub-problem in each iteration, other than solving the primal problem directly, we develop a semismooth Newton augmented Lagrangian algorithm with global linear convergence on the dual problem to improve the efficiency. Theoretical properties of our proposed algorithm have been established. In particular, we show that the convergence rate of our algorithm is asymptotically superlinear. The high efficiency and promising performance of our algorithm are illustrated via extensive simulation studies and real data applications, with comparison to several state-of-the-art solvers.
By definition, reciprocal matrices are tridiagonal $n$-by-$n$ matrices $A$ with constant main diagonal and such that $a_{i,i+1}a_{i+1,i}=1$ for $i=1,ldots,n-1$. For $nleq 6$, we establish criteria under which the numerical range generating curves (al
so called Kippenhahn curves) of such matrices consist of elliptical components only. As a corollary, we also provide a complete description of higher-rank numerical ranges when the criteria are met.
Current large-scale language models can be politically biased as a result of the data they are trained on, potentially causing serious problems when they are deployed in real-world settings. In this paper, we describe metrics for measuring political
bias in GPT-2 generation and propose a reinforcement learning (RL) framework for mitigating political biases in generated text. By using rewards from word embeddings or a classifier, our RL framework guides debiased generation without having access to the training data or requiring the model to be retrained. In empirical experiments on three attributes sensitive to political bias (gender, location, and topic), our methods reduced bias according to both our metrics and human evaluation, while maintaining readability and semantic coherence.
This paper introduces the system submitted by the DKU-SMIIP team for the Auto-KWS 2021 Challenge. Our implementation consists of a two-stage keyword spotting system based on query-by-example spoken term detection and a speaker verification system. We
employ two different detection algorithms in our proposed keyword spotting system. The first stage adopts subsequence dynamic time warping for template matching based on frame-level language-independent bottleneck feature and phoneme posterior probability. We use a sliding window template matching algorithm based on acoustic word embeddings to further verify the detection from the first stage. As a result, our KWS system achieves an average score of 0.61 on the feedback dataset, which outperforms the baseline1 system by 0.25.
