This paper investigates statistical inference for noisy matrix completion in a semi-supervised model when auxiliary covariates are available. The model consists of two parts. One part is a low-rank matrix induced by unobserved latent factors; the other part models the effects of the observed covariates through a coefficient matrix which is composed of high-dimensional column vectors. We model the observational pattern of the responses through a logistic regression of the covariates, and allow its probability to go to zero as the sample size increases. We apply an iterative least squares (LS) estimation approach in our considered context. The iterative LS methods in general enjoy a low computational cost, but deriving the statistical properties of the resulting estimators is a challenging task. We show that our method only needs a few iterations, and the resulting entry-wise estimators of the low-rank matrix and the coefficient matrix are guaranteed to have asymptotic normal distributions. As a result, individual inference can be conducted for each entry of the unknown matrices. We also propose a simultaneous testing procedure with multiplier bootstrap for the high-dimensional coefficient matrix. This simultaneous inferential tool can help us further investigate the effects of covariates for the prediction of missing entries.
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Toward desirable saliency prediction, the types and numbers of inputs for a salient object detection (SOD) algorithm may dynamically change in many real-life applications. However, existing SOD algorithms are mainly designed or trained for one particular type of inputs, failing to be generalized to other types of inputs. Consequentially, more types of SOD algorithms need to be prepared in advance for handling different types of inputs, raising huge hardware and research costs. Differently, in this paper, we propose a new type of SOD task, termed Arbitrary Modality SOD (AM SOD). The most prominent characteristics of AM SOD are that the modality types and modality numbers will be arbitrary or dynamically changed. The former means that the inputs to the AM SOD algorithm may be arbitrary modalities such as RGB, depths, or even any combination of them. While, the latter indicates that the inputs may have arbitrary modality numbers as the input type is changed, e.g. single-modality RGB image, dual-modality RGB-Depth (RGB-D) images or triple-modality RGB-Depth-Thermal (RGB-D-T) images. Accordingly, a preliminary solution to the above challenges, \i.e. a modality switch network (MSN), is proposed in this paper. In particular, a modality switch feature extractor (MSFE) is first designed to extract discriminative features from each modality effectively by introducing some modality indicators, which will generate some weights for modality switching. Subsequently, a dynamic fusion module (DFM) is proposed to adaptively fuse features from a variable number of modalities based on a novel Transformer structure. Finally, a new dataset, named AM-XD, is constructed to facilitate research on AM SOD. Extensive experiments demonstrate that our AM SOD method can effectively cope with changes in the type and number of input modalities for robust salient object detection.
We study learnability of linear utility functions from pairwise comparison queries. In particular, we consider two learning objectives. The first objective is to predict out-of-sample responses to pairwise comparisons, whereas the second is to approximately recover the true parameters of the utility function. We show that in the passive learning setting, linear utilities are efficiently learnable with respect to the first objective, both when query responses are uncorrupted by noise, and under Tsybakov noise when the distributions are sufficiently "nice". In contrast, we show that utility parameters are not learnable for a large set of data distributions without strong modeling assumptions, even when query responses are noise-free. Next, we proceed to analyze the learning problem in an active learning setting. In this case, we show that even the second objective is efficiently learnable, and present algorithms for both the noise-free and noisy query response settings. Our results thus exhibit a qualitative learnability gap between passive and active learning from pairwise preference queries, demonstrating the value of the ability to select pairwise queries for utility learning.
We optimize pipeline parallelism for deep neural network (DNN) inference by partitioning model graphs into $k$ stages and minimizing the running time of the bottleneck stage, including communication. We give practical and effective algorithms for this NP-hard problem, but our emphasis is on tackling the practitioner's dilemma of deciding when a solution is good enough. To this end, we design novel mixed-integer programming (MIP) relaxations for proving lower bounds. Applying these methods to a diverse testbed of 369 production models, for $k \in \{2, 4, 8, 16, 32, 64\}$, we empirically show that these lower bounds are strong enough to be useful in practice. Our lower bounds are substantially stronger than standard combinatorial bounds. For example, evaluated via geometric means across our production testbed with $k = 16$ pipeline stages, our MIP formulations raised the lower bound from 0.4598 to 0.9452, expressed as a fraction of the best partition found. In other words, our improved lower bounds closed the optimality gap by a factor of 9.855x.
We investigate contrastive learning in the federated setting through the lens of SimCLR and multi-view mutual information maximization. In doing so, we uncover a connection between contrastive representation learning and user verification; by adding a user verification loss to each client's local SimCLR loss we recover a lower bound to the global multi-view mutual information. To accommodate for the case of when some labelled data are available at the clients, we extend our SimCLR variant to the federated semi-supervised setting. We see that a supervised SimCLR objective can be obtained with two changes: a) the contrastive loss is computed between datapoints that share the same label and b) we require an additional auxiliary head that predicts the correct labels from either of the two views. Along with the proposed SimCLR extensions, we also study how different sources of non-i.i.d.-ness can impact the performance of federated unsupervised learning through global mutual information maximization; we find that a global objective is beneficial for some sources of non-i.i.d.-ness but can be detrimental for others. We empirically evaluate our proposed extensions in various tasks to validate our claims and furthermore demonstrate that our proposed modifications generalize to other pretraining methods.
This paper considers the beamforming optimization for sensing a point-like scatterer using a bistatic multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) radar, which could be part of a joint communication and sensing system. The goal is to minimize the Cram\'er-Rao bound on the target position's estimation error, where the radar already knows an approximate position that is taken into account in the optimization. The optimization allows for beamforming with more than one beam per subcarrier. Optimal solutions for the beamforming are discussed for known and unknown channel gain. Numerical results show that beamforming with at most one beam per subcarrier is optimal for certain parameters, but for other parameters, optimal solutions need two beams on some subcarriers. In addition, the degree of freedom in selecting which end of the bistatic radar should transmit and receive is considered.
We propose new algorithms with provable performance for online binary optimization subject to general constraints and in dynamic settings. We consider the subset of problems in which the objective function is submodular. We propose the online submodular greedy algorithm (OSGA) which solves to optimality an approximation of the previous round loss function to avoid the NP-hardness of the original problem. We extend OSGA to a generic approximation function. We show that OSGA has a dynamic regret bound similar to the tightest bounds in online convex optimization with respect to the time horizon and the cumulative round optimum variation. For instances where no approximation exists or a computationally simpler implementation is desired, we design the online submodular projected gradient descent (OSPGD) by leveraging the Lova\'sz extension. We obtain a regret bound that is akin to the conventional online gradient descent (OGD). Finally, we numerically test our algorithms in two power system applications: fast-timescale demand response and real-time distribution network reconfiguration.
Most existing temporal point process models are characterized by conditional intensity function. These models often require numerical approximation methods for likelihood evaluation, which potentially hurts their performance. By directly modelling the integral of the intensity function, i.e., the cumulative hazard function (CHF), the likelihood can be evaluated accurately, making it a promising approach. However, existing CHF-based methods are not well-defined, i.e., the mathematical constraints of CHF are not completely satisfied, leading to untrustworthy results. For multivariate temporal point process, most existing methods model intensity (or density, etc.) functions for each variate, limiting the scalability. In this paper, we explore using neural networks to model a flexible but well-defined CHF and learning the multivariate temporal point process with low parameter complexity. Experimental results on six datasets show that the proposed model achieves the state-of-the-art performance on data fitting and event prediction tasks while having significantly fewer parameters and memory usage than the strong competitors. The source code and data can be obtained from //github.com/lbq8942/NPP.
One of the most important processing steps in any analysis pipeline is handling missing data. Traditional approaches simply delete any sample or feature with missing elements. Recent imputation methods replace missing data based on assumed relationships between observed data and the missing elements. However, there is a largely under-explored alternative amid these extremes. Partial deletion approaches remove excessive amounts of missing data, as defined by the user. They can be used in place of traditional deletion or as a precursor to imputation. In this manuscript, we expand upon the Mr. Clean suite of algorithms, focusing on the scenario where all missing data is removed. We show that the RowCol Integer Program can be recast as a Linear Program, thereby reducing runtime. Additionally, the Element Integer Program can be reformulated to reduce the number of variables and allow for high levels of parallelization. Using real-world data sets from genetic, gene expression, and single cell RNA-seq experiments we demonstrate that our algorithms outperform existing deletion techniques over several missingness values, balancing runtime and data retention. Our combined greedy algorithm retains the maximum number of valid elements in 126 of 150 scenarios and stays within 1\% of maximum in 23 of the remaining experiments. The reformulated Element IP complements the greedy algorithm when removing all missing data, boasting a reduced runtime and increase in valid elements in larger data sets, over its generic counterpart. These two programs greatly increase the amount of valid data retained over traditional deletion techniques and further improve on existing partial deletion algorithms.
Disentangled Representation Learning (DRL) aims to learn a model capable of identifying and disentangling the underlying factors hidden in the observable data in representation form. The process of separating underlying factors of variation into variables with semantic meaning benefits in learning explainable representations of data, which imitates the meaningful understanding process of humans when observing an object or relation. As a general learning strategy, DRL has demonstrated its power in improving the model explainability, controlability, robustness, as well as generalization capacity in a wide range of scenarios such as computer vision, natural language processing, data mining etc. In this article, we comprehensively review DRL from various aspects including motivations, definitions, methodologies, evaluations, applications and model designs. We discuss works on DRL based on two well-recognized definitions, i.e., Intuitive Definition and Group Theory Definition. We further categorize the methodologies for DRL into four groups, i.e., Traditional Statistical Approaches, Variational Auto-encoder Based Approaches, Generative Adversarial Networks Based Approaches, Hierarchical Approaches and Other Approaches. We also analyze principles to design different DRL models that may benefit different tasks in practical applications. Finally, we point out challenges in DRL as well as potential research directions deserving future investigations. We believe this work may provide insights for promoting the DRL research in the community.
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.
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