We introduce new differentially private (DP) mechanisms for gradient-based machine learning (ML) with multiple passes (epochs) over a dataset, substantially improving the achievable privacy-utility-computation tradeoffs. We formalize the problem of DP mechanisms for adaptive streams with multiple participations and introduce a non-trivial extension of online matrix factorization DP mechanisms to our setting. This includes establishing the necessary theory for sensitivity calculations and efficient computation of optimal matrices. For some applications like $>\!\! 10,000$ SGD steps, applying these optimal techniques becomes computationally expensive. We thus design an efficient Fourier-transform-based mechanism with only a minor utility loss. Extensive empirical evaluation on both example-level DP for image classification and user-level DP for language modeling demonstrate substantial improvements over all previous methods, including the widely-used DP-SGD . Though our primary application is to ML, our main DP results are applicable to arbitrary linear queries and hence may have much broader applicability.
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This paper presents the design and development of an Anderson Accelerated Preconditioned Modified Hermitian and Skew-Hermitian Splitting (AA-PMHSS) method for solving complex-symmetric linear systems with application to electromagnetics problems, such as wave scattering and eddy currents. While it has been shown that the Anderson Acceleration of real linear systems is essentially equivalent to GMRES, we show here that the formulation using Anderson acceleration leads to a more performant method. We show relatively good robustness compared to existing preconditioned GMRES methods and significantly better performance due to the faster evaluation of the preconditioner. In particular, AA-PMHSS can be applied to solve problems and equations arising from electromagnetics, such as time-harmonic eddy current simulations discretized with the Finite Element Method. We also evaluate three test systems present in previous literature. We show that the method is competitive with two types of preconditioned GMRES. One of the significant advantages of these methods is that the convergence rate is independent of the discretization size.
Contrastive learning is a major studied topic in metric learning. However, sampling effective contrastive pairs remains a challenge due to factors such as limited batch size, imbalanced data distribution, and the risk of overfitting. In this paper, we propose a novel metric learning function called Center Contrastive Loss, which maintains a class-wise center bank and compares the category centers with the query data points using a contrastive loss. The center bank is updated in real-time to boost model convergence without the need for well-designed sample mining. The category centers are well-optimized classification proxies to re-balance the supervisory signal of each class. Furthermore, the proposed loss combines the advantages of both contrastive and classification methods by reducing intra-class variations and enhancing inter-class differences to improve the discriminative power of embeddings. Our experimental results, as shown in Figure 1, demonstrate that a standard network (ResNet50) trained with our loss achieves state-of-the-art performance and faster convergence.
Modern datasets are trending towards ever higher dimension. In response, recent theoretical studies of covariance estimation often assume the proportional-growth asymptotic framework, where the sample size $n$ and dimension $p$ are comparable, with $n, p \rightarrow \infty $ and $\gamma_n = p/n \rightarrow \gamma > 0$. Yet, many datasets -- perhaps most -- have very different numbers of rows and columns. We consider instead the disproportional-growth asymptotic framework, where $n, p \rightarrow \infty$ and $\gamma_n \rightarrow 0$ or $\gamma_n \rightarrow \infty$. Either disproportional limit induces novel behavior unseen within previous proportional and fixed-$p$ analyses. We study the spiked covariance model, with theoretical covariance a low-rank perturbation of the identity. For each of 15 different loss functions, we exhibit in closed form new optimal shrinkage and thresholding rules. Our optimal procedures demand extensive eigenvalue shrinkage and offer substantial performance benefits over the standard empirical covariance estimator. Practitioners may ask whether to view their data as arising within (and apply the procedures of) the proportional or disproportional frameworks. Conveniently, it is possible to remain {\it framework agnostic}: one unified set of closed-form shrinkage rules (depending only on the aspect ratio $\gamma_n$ of the given data) offers full asymptotic optimality under either framework. At the heart of the phenomena we explore is the spiked Wigner model, in which a low-rank matrix is perturbed by symmetric noise. Exploiting a connection to the spiked covariance model as $\gamma_n \rightarrow 0$, we derive optimal eigenvalue shrinkage rules for estimation of the low-rank component, of independent and fundamental interest.
Existing research efforts for multi-interest candidate matching in recommender systems mainly focus on improving model architecture or incorporating additional information, neglecting the importance of training schemes. This work revisits the training framework and uncovers two major problems hindering the expressiveness of learned multi-interest representations. First, the current training objective (i.e., uniformly sampled softmax) fails to effectively train discriminative representations in a multi-interest learning scenario due to the severe increase in easy negative samples. Second, a routing collapse problem is observed where each learned interest may collapse to express information only from a single item, resulting in information loss. To address these issues, we propose the REMI framework, consisting of an Interest-aware Hard Negative mining strategy (IHN) and a Routing Regularization (RR) method. IHN emphasizes interest-aware hard negatives by proposing an ideal sampling distribution and developing a Monte-Carlo strategy for efficient approximation. RR prevents routing collapse by introducing a novel regularization term on the item-to-interest routing matrices. These two components enhance the learned multi-interest representations from both the optimization objective and the composition information. REMI is a general framework that can be readily applied to various existing multi-interest candidate matching methods. Experiments on three real-world datasets show our method can significantly improve state-of-the-art methods with easy implementation and negligible computational overhead. The source code will be released.
We study a portioning setting in which a public resource such as time or money is to be divided among a given set of candidates, and each agent proposes a division of the resource. We consider two families of aggregation rules for this setting - those based on coordinate-wise aggregation and those that optimize some notion of welfare - as well as the recently proposed Independent Markets mechanism. We provide a detailed analysis of these rules from an axiomatic perspective, both for classic axioms, such as strategyproofness and Pareto optimality, and for novel axioms, which aim to capture proportionality in this setting. Our results indicate that a simple rule that computes the average of all proposals satisfies many of our axioms, including some that are violated by more sophisticated rules.
Click-through rate (CTR) prediction plays a critical role in recommender systems and online advertising. The data used in these applications are multi-field categorical data, where each feature belongs to one field. Field information is proved to be important and there are several works considering fields in their models. In this paper, we proposed a novel approach to model the field information effectively and efficiently. The proposed approach is a direct improvement of FwFM, and is named as Field-matrixed Factorization Machines (FmFM, or $FM^2$). We also proposed a new explanation of FM and FwFM within the FmFM framework, and compared it with the FFM. Besides pruning the cross terms, our model supports field-specific variable dimensions of embedding vectors, which acts as soft pruning. We also proposed an efficient way to minimize the dimension while keeping the model performance. The FmFM model can also be optimized further by caching the intermediate vectors, and it only takes thousands of floating-point operations (FLOPs) to make a prediction. Our experiment results show that it can out-perform the FFM, which is more complex. The FmFM model's performance is also comparable to DNN models which require much more FLOPs in runtime.
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple iterative methods such as gradient descent have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently. In this tutorial-style overview, we highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: (1) two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and (2) global landscape analysis and initialization-free algorithms. Several canonical matrix factorization problems are discussed, including but not limited to matrix sensing, phase retrieval, matrix completion, blind deconvolution, robust principal component analysis, phase synchronization, and joint alignment. Special care is taken to illustrate the key technical insights underlying their analyses. This article serves as a testament that the integrated consideration of optimization and statistics leads to fruitful research findings.
Few-shot Learning aims to learn classifiers for new classes with only a few training examples per class. Existing meta-learning or metric-learning based few-shot learning approaches are limited in handling diverse domains with various number of labels. The meta-learning approaches train a meta learner to predict weights of homogeneous-structured task-specific networks, requiring a uniform number of classes across tasks. The metric-learning approaches learn one task-invariant metric for all the tasks, and they fail if the tasks diverge. We propose to deal with these limitations with meta metric learning. Our meta metric learning approach consists of task-specific learners, that exploit metric learning to handle flexible labels, and a meta learner, that discovers good parameters and gradient decent to specify the metrics in task-specific learners. Thus the proposed model is able to handle unbalanced classes as well as to generate task-specific metrics. We test our approach in the `$k$-shot $N$-way' few-shot learning setting used in previous work and new realistic few-shot setting with diverse multi-domain tasks and flexible label numbers. Experiments show that our approach attains superior performances in both settings.
Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.
Learning from a few examples remains a key challenge in machine learning. Despite recent advances in important domains such as vision and language, the standard supervised deep learning paradigm does not offer a satisfactory solution for learning new concepts rapidly from little data. In this work, we employ ideas from metric learning based on deep neural features and from recent advances that augment neural networks with external memories. Our framework learns a network that maps a small labelled support set and an unlabelled example to its label, obviating the need for fine-tuning to adapt to new class types. We then define one-shot learning problems on vision (using Omniglot, ImageNet) and language tasks. Our algorithm improves one-shot accuracy on ImageNet from 87.6% to 93.2% and from 88.0% to 93.8% on Omniglot compared to competing approaches. We also demonstrate the usefulness of the same model on language modeling by introducing a one-shot task on the Penn Treebank.
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