The Gradient Boosting Decision Tree (GBDT) is a popular machine learning model for various tasks in recent years. In this paper, we study how to improve model accuracy of GBDT while preserving the strong guarantee of differential privacy. \textit{Sensitivity} and \textit{privacy budget} are two key design aspects for the effectiveness of differential private models. Existing solutions for GBDT with differential privacy suffer from the significant accuracy loss due to too loose sensitivity bounds and ineffective privacy budget allocations (especially across different trees in the GBDT model). Loose sensitivity bounds lead to more noise to obtain a fixed privacy level. Ineffective privacy budget allocations worsen the accuracy loss especially when the number of trees is large. Therefore, we propose a new GBDT training algorithm that achieves tighter sensitivity bounds and more effective noise allocations. Specifically, by investigating the property of gradient and the contribution of each tree in GBDTs, we propose to adaptively control the gradients of training data for each iteration and leaf node clipping in order to tighten the sensitivity bounds. Furthermore, we design a novel boosting framework to allocate the privacy budget between trees so that the accuracy loss can be reduced. Our experiments show that our approach can achieve much better model accuracy than other baselines.

The darknet markets are notorious black markets in cyberspace, which involve selling or brokering drugs, weapons, stolen credit cards, and other illicit goods. To combat illicit transactions in the cyberspace, it is important to analyze the behaviors of participants in darknet markets. Currently, many studies focus on studying the behavior of vendors. However, there is no much work on analyzing buyers. The key challenge is that the buyers are anonymized in darknet markets. For most of the darknet markets, We only observe the first and last digits of a buyer's ID, such as ``a**b''. To tackle this challenge, we propose a hidden buyer identification model, called UNMIX, which can group the transactions from one hidden buyer into one cluster given a transaction sequence from an anonymized ID. UNMIX is able to model the temporal dynamics information as well as the product, comment, and vendor information associated with each transaction. As a result, the transactions with similar patterns in terms of time and content group together as the subsequence from one hidden buyer. Experiments on the data collected from three real-world darknet markets demonstrate the effectiveness of our approach measured by various clustering metrics. Case studies on real transaction sequences explicitly show that our approach can group transactions with similar patterns into the same clusters.

In this article, we propose a novel probabilistic framework to improve the accuracy of a weighted majority voting algorithm. In order to assign higher weights to the classifiers which can correctly classify hard-to-classify instances, we introduce the Item Response Theory (IRT) framework to evaluate the samples' difficulty and classifiers' ability simultaneously. Three models are created with different assumptions suitable for different cases. When making an inference, we keep a balance between the accuracy and complexity. In our experiment, all the base models are constructed by single trees via bootstrap. To explain the models, we illustrate how the IRT ensemble model constructs the classifying boundary. We also compare their performance with other widely used methods and show that our model performs well on 19 datasets.

In this paper, we discuss the statistical properties of the $\ell_q$ optimization methods $(0

Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can outperform classical state-of-the-art methods in the near term. QAOA is a hybrid quantum-classical algorithm that combines a parameterized quantum state evolution with a classical optimization routine to approximately solve combinatorial problems. The quality of the solution obtained by QAOA within a fixed budget of calls to the quantum computer depends on the performance of the classical optimization routine used to optimize the variational parameters. In this work, we propose an approach based on reinforcement learning (RL) to train a policy network that can be used to quickly find high-quality variational parameters for unseen combinatorial problem instances. The RL agent is trained on small problem instances which can be simulated on a classical computer, yet the learned RL policy is generalizable and can be used to efficiently solve larger instances. Extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our trained RL policy can reduce the optimality gap by a factor up to 8.61 compared with other off-the-shelf optimizers tested.

Recurrent neural networks (RNNs) have gained a great deal of attention in solving sequential learning problems. The learning of long-term dependencies, however, remains challenging due to the problem of a vanishing or exploding hidden states gradient. By exploring further the recently established connections between RNNs and dynamical systems we propose a novel RNN architecture, which we call a Hamiltonian recurrent neural network (Hamiltonian RNN), based on a symplectic discretization of an appropriately chosen Hamiltonian system. The key benefit of this approach is that the corresponding RNN inherits the favorable long time properties of the Hamiltonian system, which in turn allows us to control the hidden states gradient with a hyperparameter of the Hamiltonian RNN architecture. This enables us to handle sequential learning problems with arbitrary sequence lengths, since for a range of values of this hyperparameter the gradient neither vanishes nor explodes. Additionally, we provide a heuristic for the optimal choice of the hyperparameter, which we use in our numerical simulations to illustrate that the Hamiltonian RNN is able to outperform other state-of-the-art RNNs without the need of computationally intensive hyperparameter optimization.

We propose an approach that connects recurrent networks with different orders of hidden interaction with regular grammars of different levels of complexity. We argue that the correspondence between recurrent networks and formal computational models gives understanding to the analysis of the complicated behaviors of recurrent networks. We introduce an entropy value that categorizes all regular grammars into three classes with different levels of complexity, and show that several existing recurrent networks match grammars from either all or partial classes. As such, the differences between regular grammars reveal the different properties of these models. We also provide a unification of all investigated recurrent networks. Our evaluation shows that the unified recurrent network has improved performance in learning grammars, and demonstrates comparable performance on a real-world dataset with more complicated models.

Deep neural networks (DNNs) are vulnerable to subtle adversarial perturbations applied to the input. These adversarial perturbations, though imperceptible, can easily mislead the DNN. In this work, we take a control theoretic approach to the problem of robustness in DNNs. We treat each individual layer of the DNN as a nonlinear dynamical system and use Lyapunov theory to prove stability and robustness locally. We then proceed to prove stability and robustness globally for the entire DNN. We develop empirically tight bounds on the response of the output layer, or any hidden layer, to adversarial perturbations added to the input, or the input of hidden layers. Recent works have proposed spectral norm regularization as a solution for improving robustness against l2 adversarial attacks. Our results give new insights into how spectral norm regularization can mitigate the adversarial effects. Finally, we evaluate the power of our approach on a variety of data sets and network architectures and against some of the well-known adversarial attacks.

Markov blanket feature selection, while theoretically optimal, generally is challenging to implement. This is due to the shortcomings of existing approaches to conditional independence (CI) testing, which tend to struggle either with the curse of dimensionality or computational complexity. We propose a novel two-step approach which facilitates Markov blanket feature selection in high dimensions. First, neural networks are used to map features to low-dimensional representations. In the second step, CI testing is performed by applying the k-NN conditional mutual information estimator to the learned feature maps. The mappings are designed to ensure that mapped samples both preserve information and share similar information about the target variable if and only if they are close in Euclidean distance. We show that these properties boost the performance of the k-NN estimator in the second step. The performance of the proposed method is evaluated on synthetic, as well as real data pertaining to datacenter hard disk drive failures.

Probabilistic vehicle trajectory prediction is essential for robust safety of autonomous driving. Current methods for long-term trajectory prediction cannot guarantee the physical feasibility of predicted distribution. Moreover, their models cannot adapt to the driving policy of the predicted target human driver. In this work, we propose to overcome these two shortcomings by a Bayesian recurrent neural network model consisting of Bayesian-neural-network-based policy model and known physical model of the scenario. Bayesian neural network can ensemble complicated output distribution, enabling rich family of trajectory distribution. The embedded physical model ensures feasibility of the distribution. Moreover, the adopted gradient-based training method allows direct optimization for better performance in long prediction horizon. Furthermore, a particle-filter-based parameter adaptation algorithm is designed to adapt the policy Bayesian neural network to the predicted target online. Effectiveness of the proposed methods is verified with a toy example with multi-modal stochastic feedback gain and naturalistic car following data.