We show direct and conceptually simple reductions between the classical learning with errors (LWE) problem and its continuous analog, CLWE (Bruna, Regev, Song and Tang, STOC 2021). This allows us to bring to bear the powerful machinery of LWE-based cryptography to the applications of CLWE. For example, we obtain the hardness of CLWE under the classical worst-case hardness of the gap shortest vector problem. Previously, this was known only under quantum worst-case hardness of lattice problems. More broadly, with our reductions between the two problems, any future developments to LWE will also apply to CLWE and its downstream applications. As a concrete application, we show an improved hardness result for density estimation for mixtures of Gaussians. In this computational problem, given sample access to a mixture of Gaussians, the goal is to output a function that estimates the density function of the mixture. Under the (plausible and widely believed) exponential hardness of the classical LWE problem, we show that Gaussian mixture density estimation in $\mathbb{R}^n$ with roughly $\log n$ Gaussian components given $\mathsf{poly}(n)$ samples requires time quasi-polynomial in $n$. Under the (conservative) polynomial hardness of LWE, we show hardness of density estimation for $n^{\epsilon}$ Gaussians for any constant $\epsilon > 0$, which improves on Bruna, Regev, Song and Tang (STOC 2021), who show hardness for at least $\sqrt{n}$ Gaussians under polynomial (quantum) hardness assumptions. Our key technical tool is a reduction from classical LWE to LWE with $k$-sparse secrets where the multiplicative increase in the noise is only $O(\sqrt{k})$, independent of the ambient dimension $n$.
Extreme precipitation wreaks havoc throughout the world, causing billions of dollars in damage and uprooting communities, ecosystems, and economies. Accurate extreme precipitation prediction allows more time for preparation and disaster risk management for such extreme events. In this paper, we focus on short-term extreme precipitation forecasting (up to a 12-hour ahead-of-time prediction) from a sequence of sea level pressure and zonal wind anomalies. Although existing machine learning approaches have shown promising results, the associated model and climate uncertainties may reduce their reliability. To address this issue, we propose a self-attention augmented convolution mechanism for extreme precipitation forecasting, systematically combining attention scores with traditional convolutions to enrich feature data and reduce the expected errors of the results. The proposed network architecture is further fused with a highway neural network layer to gain the benefits of unimpeded information flow across several layers. Our experimental results show that the framework outperforms classical convolutional models by 12%. The proposed method increases machine learning as a tool for gaining insights into the physical causes of changing extremes, lowering uncertainty in future forecasts.
We consider the problem of combining and learning over a set of adversarial bandit algorithms with the goal of adaptively tracking the best one on the fly. The CORRAL algorithm of Agarwal et al. (2017) and its variants (Foster et al., 2020a) achieve this goal with a regret overhead of order $\widetilde{O}(\sqrt{MT})$ where $M$ is the number of base algorithms and $T$ is the time horizon. The polynomial dependence on $M$, however, prevents one from applying these algorithms to many applications where $M$ is poly$(T)$ or even larger. Motivated by this issue, we propose a new recipe to corral a larger band of bandit algorithms whose regret overhead has only \emph{logarithmic} dependence on $M$ as long as some conditions are satisfied. As the main example, we apply our recipe to the problem of adversarial linear bandits over a $d$-dimensional $\ell_p$ unit-ball for $p \in (1,2]$. By corralling a large set of $T$ base algorithms, each starting at a different time step, our final algorithm achieves the first optimal switching regret $\widetilde{O}(\sqrt{d S T})$ when competing against a sequence of comparators with $S$ switches (for some known $S$). We further extend our results to linear bandits over a smooth and strongly convex domain as well as unconstrained linear bandits.
Detailed information about individual claims are completely ignored when insurance claims data are aggregated and structured in development triangles for loss reserving. In the hope of extracting predictive power from the individual claims characteristics, researchers have recently proposed to move away from these macro-level methods in favor of micro-level loss reserving approaches. We introduce a discrete-time individual reserving framework incorporating granular information in a deep learning approach named Long Short-Term Memory (LSTM) neural network. At each time period, the network has two tasks: first, classifying whether there is a payment or a recovery, and second, predicting the corresponding non-zero amount, if any. We illustrate the estimation procedure on a simulated and a real general insurance dataset. We compare our approach with the chain-ladder aggregate method using the predictive outstanding loss estimates and their actual values. Based on a generalized Pareto model for excess payments over a threshold, we adjust the LSTM reserve prediction to account for extreme payments.
Deep learning models have introduced various intelligent applications to edge devices, such as image classification, speech recognition, and augmented reality. There is an increasing need of training such models on the devices in order to deliver personalized, responsive, and private learning. To address this need, this paper presents a new solution for deploying and training state-of-the-art models on the resource-constrained devices. First, the paper proposes a novel filter-pruning-based model compression method to create lightweight trainable models from large models trained in the cloud, without much loss of accuracy. Second, it proposes a novel knowledge transfer method to enable the on-device model to update incrementally in real time or near real time using incremental learning on new data and enable the on-device model to learn the unseen categories with the help of the in-cloud model in an unsupervised fashion. The results show that 1) our model compression method can remove up to 99.36% parameters of WRN-28-10, while preserving a Top-1 accuracy of over 90% on CIFAR-10; 2) our knowledge transfer method enables the compressed models to achieve more than 90% accuracy on CIFAR-10 and retain good accuracy on old categories; 3) it allows the compressed models to converge within real time (three to six minutes) on the edge for incremental learning tasks; 4) it enables the model to classify unseen categories of data (78.92% Top-1 accuracy) that it is never trained with.
Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control methods. However, designing an appropriate Koopman embedding function remains a challenging task. Furthermore, most Koopman-based algorithms only consider nonlinear systems with linear control input, resulting in lousy prediction and control performance when the system is fully nonlinear with the control input. In this work, we propose an end-to-end deep learning framework to learn the Koopman embedding function and Koopman Operator together to alleviate such difficulties. We first parameterize the embedding function and Koopman Operator with the neural network and train them end-to-end with the K-steps loss function. We then design an auxiliary control network to encode the nonlinear state-dependent control term to model the nonlinearity in control input. For linear control, this encoded term is considered the new control variable instead, ensuring the linearity of the embedding space. Then we deploy Linear Quadratic Regulator (LQR) on the linear embedding space to derive the optimal control policy and decode the actual control input from the control net. Experimental results demonstrate that our approach outperforms other existing methods, reducing the prediction error by order-of-magnitude and achieving superior control performance in several nonlinear dynamic systems like damping pendulum, CartPole, and 7 Dof robotic manipulator.
Vision transformers (ViTs) have recently set off a new wave in neural architecture design thanks to their record-breaking performance in various vision tasks. In parallel, to fulfill the goal of deploying ViTs into real-world vision applications, their robustness against potential malicious attacks has gained increasing attention. In particular, recent works show that ViTs are more robust against adversarial attacks as compared with convolutional neural networks (CNNs), and conjecture that this is because ViTs focus more on capturing global interactions among different input/feature patches, leading to their improved robustness to local perturbations imposed by adversarial attacks. In this work, we ask an intriguing question: "Under what kinds of perturbations do ViTs become more vulnerable learners compared to CNNs?" Driven by this question, we first conduct a comprehensive experiment regarding the robustness of both ViTs and CNNs under various existing adversarial attacks to understand the underlying reason favoring their robustness. Based on the drawn insights, we then propose a dedicated attack framework, dubbed Patch-Fool, that fools the self-attention mechanism by attacking its basic component (i.e., a single patch) with a series of attention-aware optimization techniques. Interestingly, our Patch-Fool framework shows for the first time that ViTs are not necessarily more robust than CNNs against adversarial perturbations. In particular, we find that ViTs are more vulnerable learners compared with CNNs against our Patch-Fool attack which is consistent across extensive experiments, and the observations from Sparse/Mild Patch-Fool, two variants of Patch-Fool, indicate an intriguing insight that the perturbation density and strength on each patch seem to be the key factors that influence the robustness ranking between ViTs and CNNs.
We consider regret minimization for online control with time-varying linear dynamical systems. The metric of performance we study is adaptive policy regret, or regret compared to the best policy on {\it any interval in time}. We give an efficient algorithm that attains first-order adaptive regret guarantees for the setting of online convex optimization with memory. We also show that these first-order bounds are nearly tight. This algorithm is then used to derive a controller with adaptive regret guarantees that provably competes with the best linear controller on any interval in time. We validate these theoretical findings experimentally on simulations of time-varying dynamics and disturbances.
While recent automated data augmentation methods lead to state-of-the-art results, their design spaces and the derived data augmentation strategies still incorporate strong human priors. In this work, instead of fixing a set of hand-picked default augmentations alongside the searched data augmentations, we propose a fully automated approach for data augmentation search named Deep AutoAugment (DeepAA). DeepAA progressively builds a multi-layer data augmentation pipeline from scratch by stacking augmentation layers one at a time until reaching convergence. For each augmentation layer, the policy is optimized to maximize the cosine similarity between the gradients of the original and augmented data along the direction with low variance. Our experiments show that even without default augmentations, we can learn an augmentation policy that achieves strong performance with that of previous works. Extensive ablation studies show that the regularized gradient matching is an effective search method for data augmentation policies. Our code is available at: https://github.com/MSU-MLSys-Lab/DeepAA .
Money laundering is the crucial mechanism utilized by criminals to inject proceeds of crime to the financial system. The primary responsibility of the detection of suspicious activity related to money laundering is with the financial institutions. Most of the current systems in these institutions are rule-based and ineffective. The available data science-based anti-money laundering (AML) models in order to replace the existing rule-based systems work on customer relationship management (CRM) features and time characteristics of transaction behaviour. However, there is still a challenge on accuracy and problems around feature engineering due to thousands of possible features. Aiming to improve the detection performance of suspicious transaction monitoring systems for AML systems, in this article, we introduce a novel feature set based on time-frequency analysis, that makes use of 2-D representations of financial transactions. Random forest is utilized as a machine learning method, and simulated annealing is adopted for hyperparameter tuning. The designed algorithm is tested on real banking data, proving the efficacy of the results in practically relevant environments. It is shown that the time-frequency characteristics of suspicious and non-suspicious entities differentiate significantly, which would substantially improve the precision of data science-based transaction monitoring systems looking at only time-series transaction and CRM features.