Protecting the privacy of people whose data is used by machine learning algorithms is important. Differential Privacy is the appropriate mathematical framework for formal guarantees of privacy, and boosted decision trees are a popular machine learning technique. So we propose and test a practical algorithm for boosting decision trees that guarantees differential privacy. Privacy is enforced because our booster never puts too much weight on any one example; this ensures that each individual's data never influences a single tree "too much." Experiments show that this boosting algorithm can produce better model sparsity and accuracy than other differentially private ensemble classifiers.
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Anomaly detection among a large number of processes arises in many applications ranging from dynamic spectrum access to cybersecurity. In such problems one can often obtain noisy observations aggregated from a chosen subset of processes that conforms to a tree structure. The distribution of these observations, based on which the presence of anomalies is detected, may be only partially known. This gives rise to the need for a search strategy designed to account for both the sample complexity and the detection accuracy, as well as cope with statistical models that are known only up to some missing parameters. In this work we propose a sequential search strategy using two variations of the Generalized Local Likelihood Ratio statistic. Our proposed Hierarchical Dynamic Search (HDS) strategy is shown to be order-optimal with respect to the size of the search space and asymptotically optimal with respect to the detection accuracy. An explicit upper bound on the error probability of HDS is established for the finite sample regime. Extensive experiments are conducted, demonstrating the performance gains of HDS over existing methods.
Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guaranteeing privacy in data sharing, the known mechanisms to achieve it come with some serious limitations. Utility guarantees are usually provided only for a fixed, a priori specified set of queries. Moreover, there are no utility guarantees for more complex - but very common - machine learning tasks such as clustering or classification. In this paper we overcome some of these limitations. Working with metric privacy, a powerful generalization of differential privacy, we develop a polynomial-time algorithm that creates a private measure from a data set. This private measure allows us to efficiently construct private synthetic data that are accurate for a wide range of statistical analysis tools. Moreover, we prove an asymptotically sharp min-max result for private measures and synthetic data for general compact metric spaces. A key ingredient in our construction is a new superregular random walk, whose joint distribution of steps is as regular as that of independent random variables, yet which deviates from the origin logarithmicaly slowly.
Due to the high human cost of annotation, it is non-trivial to curate a large-scale medical dataset that is fully labeled for all classes of interest. Instead, it would be convenient to collect multiple small partially labeled datasets from different matching sources, where the medical images may have only been annotated for a subset of classes of interest. This paper offers an empirical understanding of an under-explored problem, namely partially supervised multi-label classification (PSMLC), where a multi-label classifier is trained with only partially labeled medical images. In contrast to the fully supervised counterpart, the partial supervision caused by medical data scarcity has non-trivial negative impacts on the model performance. A potential remedy could be augmenting the partial labels. Though vicinal risk minimization (VRM) has been a promising solution to improve the generalization ability of the model, its application to PSMLC remains an open question. To bridge the methodological gap, we provide the first VRM-based solution to PSMLC. The empirical results also provide insights into future research directions on partially supervised learning under data scarcity.
The emerging public awareness and government regulations of data privacy motivate new paradigms of collecting and analyzing data that are transparent and acceptable to data owners. We present a new concept of privacy and corresponding data formats, mechanisms, and theories for privatizing data during data collection. The privacy, named Interval Privacy, enforces the raw data conditional distribution on the privatized data to be the same as its unconditional distribution over a nontrivial support set. Correspondingly, the proposed privacy mechanism will record each data value as a random interval (or, more generally, a range) containing it. The proposed interval privacy mechanisms can be easily deployed through survey-based data collection interfaces, e.g., by asking a respondent whether its data value is within a randomly generated range. Another unique feature of interval mechanisms is that they obfuscate the truth but do not perturb it. Using narrowed range to convey information is complementary to the popular paradigm of perturbing data. Also, the interval mechanisms can generate progressively refined information at the discretion of individuals, naturally leading to privacy-adaptive data collection. We develop different aspects of theory such as composition, robustness, distribution estimation, and regression learning from interval-valued data. Interval privacy provides a new perspective of human-centric data privacy where individuals have a perceptible, transparent, and simple way of sharing sensitive data.
We study online convex optimization with switching costs, a practically important but also extremely challenging problem due to the lack of complete offline information. By tapping into the power of machine learning (ML) based optimizers, ML-augmented online algorithms (also referred to as expert calibration in this paper) have been emerging as state of the art, with provable worst-case performance guarantees. Nonetheless, by using the standard practice of training an ML model as a standalone optimizer and plugging it into an ML-augmented algorithm, the average cost performance can be even worse than purely using ML predictions. In order to address the "how to learn" challenge, we propose EC-L2O (expert-calibrated learning to optimize), which trains an ML-based optimizer by explicitly taking into account the downstream expert calibrator. To accomplish this, we propose a new differentiable expert calibrator that generalizes regularized online balanced descent and offers a provably better competitive ratio than pure ML predictions when the prediction error is large. For training, our loss function is a weighted sum of two different losses -- one minimizing the average ML prediction error for better robustness, and the other one minimizing the post-calibration average cost. We also provide theoretical analysis for EC-L2O, highlighting that expert calibration can be even beneficial for the average cost performance and that the high-percentile tail ratio of the cost achieved by EC-L2O to that of the offline optimal oracle (i.e., tail cost ratio) can be bounded. Finally, we test EC-L2O by running simulations for sustainable datacenter demand response. Our results demonstrate that EC-L2O can empirically achieve a lower average cost as well as a lower competitive ratio than the existing baseline algorithms.
We provide a decision theoretic analysis of bandit experiments. The setting corresponds to a dynamic programming problem, but solving this directly is typically infeasible. Working within the framework of diffusion asymptotics, we define suitable notions of asymptotic Bayes and minimax risk for bandit experiments. For normally distributed rewards, the minimal Bayes risk can be characterized as the solution to a nonlinear second-order partial differential equation (PDE). Using a limit of experiments approach, we show that this PDE characterization also holds asymptotically under both parametric and non-parametric distribution of the rewards. The approach further describes the state variables it is asymptotically sufficient to restrict attention to, and therefore suggests a practical strategy for dimension reduction. The upshot is that we can approximate the dynamic programming problem defining the bandit experiment with a PDE which can be efficiently solved using sparse matrix routines. We derive the optimal Bayes and minimax policies from the numerical solutions to these equations. The proposed policies substantially dominate existing methods such as Thompson sampling. The framework also allows for substantial generalizations to the bandit problem such as time discounting and pure exploration motives.
Boundary discontinuity and its inconsistency to the final detection metric have been the bottleneck for rotating detection regression loss design. In this paper, we propose a novel regression loss based on Gaussian Wasserstein distance as a fundamental approach to solve the problem. Specifically, the rotated bounding box is converted to a 2-D Gaussian distribution, which enables to approximate the indifferentiable rotational IoU induced loss by the Gaussian Wasserstein distance (GWD) which can be learned efficiently by gradient back-propagation. GWD can still be informative for learning even there is no overlapping between two rotating bounding boxes which is often the case for small object detection. Thanks to its three unique properties, GWD can also elegantly solve the boundary discontinuity and square-like problem regardless how the bounding box is defined. Experiments on five datasets using different detectors show the effectiveness of our approach. Codes are available at //github.com/yangxue0827/RotationDetection and //github.com/open-mmlab/mmrotate.
Vector Perturbation Precoding (VPP) can speed up downlink data transmissions in Large and Massive Multi-User MIMO systems but is known to be NP-hard. While there are several algorithms in the literature for VPP under total power constraint, they are not applicable for VPP under per-antenna power constraint. This paper proposes a novel, parallel tree search algorithm for VPP under per-antenna power constraint, called \emph{\textbf{TreeStep}}, to find good quality solutions to the VPP problem with practical computational complexity. We show that our method can provide huge performance gain over simple linear precoding like Regularised Zero Forcing. We evaluate TreeStep for several large MIMO~($16\times16$ and $24\times24$) and massive MIMO~($16\times32$ and $24\times 48$) and demonstrate that TreeStep outperforms the popular polynomial-time VPP algorithm, the Fixed Complexity Sphere Encoder, by achieving the extremely low BER of $10^{-6}$ at a much lower SNR.
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal likelihood (model evidence), which is computationally challenging, prohibiting its use in many high-dimensional Bayesian inverse problems. With Bayesian imaging applications in mind, in this work we present the proximal nested sampling methodology to objectively compare alternative Bayesian imaging models for applications that use images to inform decisions under uncertainty. The methodology is based on nested sampling, a Monte Carlo approach specialised for model comparison, and exploits proximal Markov chain Monte Carlo techniques to scale efficiently to large problems and to tackle models that are log-concave and not necessarily smooth (e.g., involving l_1 or total-variation priors). The proposed approach can be applied computationally to problems of dimension O(10^6) and beyond, making it suitable for high-dimensional inverse imaging problems. It is validated on large Gaussian models, for which the likelihood is available analytically, and subsequently illustrated on a range of imaging problems where it is used to analyse different choices of dictionary and measurement model.
Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit the given data to reveal the underlying cluster structure. Some types of losses---such as k-means, or its non-linear version: kernelized k-means (centroid based), and DBSCAN (density based)---are popular choices due to their good empirical performance on a range of applications. Although every so often the clustering output using these standard losses fails to reveal the underlying structure, and the practitioner has to custom-design their own variation. In this work we take an intrinsically different approach to clustering: rather than fitting a dataset to a specific clustering loss, we train a recurrent model that learns how to cluster. The model uses as training pairs examples of datasets (as input) and its corresponding cluster identities (as output). By providing multiple types of training datasets as inputs, our model has the ability to generalize well on unseen datasets (new clustering tasks). Our experiments reveal that by training on simple synthetically generated datasets or on existing real datasets, we can achieve better clustering performance on unseen real-world datasets when compared with standard benchmark clustering techniques. Our meta clustering model works well even for small datasets where the usual deep learning models tend to perform worse.
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