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Although generative facial prior and geometric prior have recently demonstrated high-quality results for blind face restoration, producing fine-grained facial details faithful to inputs remains a challenging problem. Motivated by the classical dictionary-based methods and the recent vector quantization (VQ) technique, we propose a VQ-based face restoration method - VQFR. VQFR takes advantage of high-quality low-level feature banks extracted from high-quality faces and can thus help recover realistic facial details. However, the simple application of the VQ codebook cannot achieve good results with faithful details and identity preservation. Therefore, we further introduce two special network designs. 1). We first investigate the compression patch size in the VQ codebook and find that the VQ codebook designed with a proper compression patch size is crucial to balance the quality and fidelity. 2). To further fuse low-level features from inputs while not "contaminating" the realistic details generated from the VQ codebook, we proposed a parallel decoder consisting of a texture decoder and a main decoder. Those two decoders then interact with a texture warping module with deformable convolution. Equipped with the VQ codebook as a facial detail dictionary and the parallel decoder design, the proposed VQFR can largely enhance the restored quality of facial details while keeping the fidelity to previous methods.

Inspired by several delay-bounded mission-critical applications, optimizing the end-to-end reliability of multi-hop networks is an important problem subject to end-to-end delay constraints on the packets. Towards that direction, Automatic Repeat Request (ARQ) based strategies have been recently proposed wherein the problem statement is to distribute a certain total number of ARQs (that capture end-to-end delay) across the nodes such that the end-to-end reliability is optimized. Although such strategies provide a fine control to trade end-to-end delay with end-to-end reliability, their performance degrades in slowly-varying channel conditions. Pointing at this drawback, in this work, we propose a Chase Combing Hybrid ARQ (CC-HARQ) based multi-hop network addressing the problem statement of how to distribute a certain total number of ARQs such that the end-to-end reliability is optimized. Towards solving the problem, first we identify that the objective function of the optimization problem is intractable due to the presence of Marcum-Q functions in it. As a result, we propose an approximation on the objective function and then prove a set of necessary and sufficient conditions on the near-optimal ARQ distribution. Subsequently, we propose a low-complexity algorithm to solve the problem for any network size. We show that CC-HARQ based strategies are particularly appealing in slow-fading channels wherein the existing ARQ strategies fail.

Centrality measures for simple graphs are well-defined and several main-memory algorithms exist for each. Simple graphs are not adequate for modeling complex data sets with multiple entities and relationships. Multilayer networks (MLNs) have been shown to be better suited, but there are very few algorithms for centrality computation directly on MLNs. They are converted (aggregated or collapsed) to simple graphs using Boolean AND or OR operators to compute centrality, which is not only inefficient but incurs a loss of structure and semantics. In this paper, we propose algorithms that compute closeness centrality on an MLN directly using a novel decoupling-based approach. Individual results of layers (or simple graphs) of an MLN are used and a composition function developed to compute the centrality for the MLN. The challenge is to do this accurately and efficiently. However, since these algorithms do not have complete information of the MLN, computing a global measure such as closeness centrality is a challenge. Hence, these algorithms rely on heuristics derived from intuition. The advantage is that this approach lends itself to parallelism and is more efficient compared to the traditional approach. We present two heuristics for composition and experimentally validate accuracy and efficiency on a large number of synthetic and real-world graphs with diverse characteristics.

It is a well-known fact that there is no complete and discrete invariant on the collection of all multiparameter persistence modules. Nonetheless, many invariants have been proposed in the literature to study multiparameter persistence modules, though each invariant will lose some amount of information. One such invariant is the generalized rank invariant. This invariant is known to be complete on the class of interval decomposable persistence modules in general, under mild assumptions on the indexing poset $P$. There is often a trade-off, where the stronger an invariant is, the more expensive it is to compute in practice. The generalized rank invariant on its own is difficult to compute, whereas the standard rank invariant is readily computable through software implementations such as RIVET. We can interpolate between these two to induce new invariants via restricting the domain of the generalized rank invariant, and this family exhibits the aforementioned trade-off. This work studies the tension which exists between computational efficiency and retaining strength when restricting the domain of the generalized rank invariant. We provide a characterization result on where such restrictions are complete invariants in the setting where $P$ is finite, and furthermore show that such restricted generalized rank invariants are stable.

We consider the problem of joint simultaneous confidence band (JSCB) construction for regression coefficient functions of time series scalar-on-function linear regression when the regression model is estimated by roughness penalization approach with flexible choices of orthonormal basis functions. A simple and unified multiplier bootstrap methodology is proposed for the JSCB construction which is shown to achieve the correct coverage probability asymptotically. Furthermore, the JSCB is asymptotically robust to inconsistently estimated standard deviations of the model. The proposed methodology is applied to a time series data set of electricity market to visually investigate and formally test the overall regression relationship as well as perform model validation. A uniform Gaussian approximation and comparison result over all Euclidean convex sets for normalized sums of a class of moderately high-dimensional stationary time series is established. Finally, the proposed methodology can be applied to simultaneous inference for scalar-on-function linear regression of independent cross-sectional data.

Bayesian optimization (BO) is a widely popular approach for the hyperparameter optimization (HPO) in machine learning. At its core, BO iteratively evaluates promising configurations until a user-defined budget, such as wall-clock time or number of iterations, is exhausted. While the final performance after tuning heavily depends on the provided budget, it is hard to pre-specify an optimal value in advance. In this work, we propose an effective and intuitive termination criterion for BO that automatically stops the procedure if it is sufficiently close to the global optimum. Our key insight is that the discrepancy between the true objective (predictive performance on test data) and the computable target (validation performance) suggests stopping once the suboptimality in optimizing the target is dominated by the statistical estimation error. Across an extensive range of real-world HPO problems and baselines, we show that our termination criterion achieves a better trade-off between the test performance and optimization time. Additionally, we find that overfitting may occur in the context of HPO, which is arguably an overlooked problem in the literature, and show how our termination criterion helps to mitigate this phenomenon on both small and large datasets.

In this paper, we introduce a novel method of neural network weight compression. In our method, we store weight tensors as sparse, quantized matrix factors, whose product is computed on the fly during inference to generate the target model's weights. We use projected gradient descent methods to find quantized and sparse factorization of the weight tensors. We show that this approach can be seen as a unification of weight SVD, vector quantization, and sparse PCA. Combined with end-to-end fine-tuning our method exceeds or is on par with previous state-of-the-art methods in terms of the trade-off between accuracy and model size. Our method is applicable to both moderate compression regimes, unlike vector quantization, and extreme compression regimes.

Relying on deep supervised or self-supervised learning, previous methods for depth completion from paired single image and sparse depth data have achieved impressive performance in recent years. However, facing a new environment where the test data occurs online and differs from the training data in the RGB image content and depth sparsity, the trained model might suffer severe performance drop. To encourage the trained model to work well in such conditions, we expect it to be capable of adapting to the new environment continuously and effectively. To achieve this, we propose MetaComp. It utilizes the meta-learning technique to simulate adaptation policies during the training phase, and then adapts the model to new environments in a self-supervised manner in testing. Considering that the input is multi-modal data, it would be challenging to adapt a model to variations in two modalities simultaneously, due to significant differences in structure and form of the two modal data. Therefore, we further propose to disentangle the adaptation procedure in the basic meta-learning training into two steps, the first one focusing on the depth sparsity while the second attending to the image content. During testing, we take the same strategy to adapt the model online to new multi-modal data. Experimental results and comprehensive ablations show that our MetaComp is capable of adapting to the depth completion in a new environment effectively and robust to changes in different modalities.

Deep learning-based image reconstruction approaches have demonstrated impressive empirical performance in many imaging modalities. These approaches usually require a large amount of high-quality paired training data, which is often not available in medical imaging. To circumvent this issue we develop a novel unsupervised knowledge-transfer paradigm for learned reconstruction within a Bayesian framework. The proposed approach learns a reconstruction network in two phases. The first phase trains a reconstruction network with a set of ordered pairs comprising of ground truth images of ellipses and the corresponding simulated measurement data. The second phase fine-tunes the pretrained network to more realistic measurement data without supervision. By construction, the framework is capable of delivering predictive uncertainty information over the reconstructed image. We present extensive experimental results on low-dose and sparse-view computed tomography showing that the approach is competitive with several state-of-the-art supervised and unsupervised reconstruction techniques. Moreover, for test data distributed differently from the training data, the proposed framework can significantly improve reconstruction quality not only visually, but also quantitatively in terms of PSNR and SSIM, when compared with learned methods trained on the synthetic dataset only.

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.