In this work we study generalization of neural networks in gradient-based meta-learning by analyzing various properties of the objective landscapes. We experimentally demonstrate that as meta-training progresses, the meta-test solutions, obtained after adapting the meta-train solution of the model, to new tasks via few steps of gradient-based fine-tuning, become flatter, lower in loss, and further away from the meta-train solution. We also show that those meta-test solutions become flatter even as generalization starts to degrade, thus providing an experimental evidence against the correlation between generalization and flat minima in the paradigm of gradient-based meta-leaning. Furthermore, we provide empirical evidence that generalization to new tasks is correlated with the coherence between their adaptation trajectories in parameter space, measured by the average cosine similarity between task-specific trajectory directions, starting from a same meta-train solution. We also show that coherence of meta-test gradients, measured by the average inner product between the task-specific gradient vectors evaluated at meta-train solution, is also correlated with generalization. Based on these observations, we propose a novel regularizer for MAML and provide experimental evidence for its effectiveness.

Financial transactions can be considered edges in a heterogeneous graph between entities sending money and entities receiving money. For financial institutions, such a graph is likely large (with millions or billions of edges) while also sparsely connected. It becomes challenging to apply machine learning to such large and sparse graphs. Graph representation learning seeks to embed the nodes of a graph into a Euclidean vector space such that graph topological properties are preserved after the transformation. In this paper, we present a novel application of representation learning to bipartite graphs of credit card transactions in order to learn embeddings of account and merchant entities. Our framework is inspired by popular approaches in graph embeddings and is trained on two internal transaction datasets. This approach yields highly effective embeddings, as quantified by link prediction AUC and F1 score. Further, the resulting entity vectors retain intuitive semantic similarity that is explored through visualizations and other qualitative analyses. Finally, we show how these embeddings can be used as features in downstream machine learning business applications such as fraud detection.

Privacy has raised considerable concerns recently, especially with the advent of information explosion and numerous data mining techniques to explore the information inside large volumes of data. In this context, a new distributed learning paradigm termed federated learning becomes prominent recently to tackle the privacy issues in distributed learning, where only learning models will be transmitted from the distributed nodes to servers without revealing users' own data and hence protecting the privacy of users. In this paper, we propose a horizontal federated XGBoost algorithm to solve the federated anomaly detection problem, where the anomaly detection aims to identify abnormalities from extremely unbalanced datasets and can be considered as a special classification problem. Our proposed federated XGBoost algorithm incorporates data aggregation and sparse federated update processes to balance the tradeoff between privacy and learning performance. In particular, we introduce the virtual data sample by aggregating a group of users' data together at a single distributed node. We compute parameters based on these virtual data samples in the local nodes and aggregate the learning model in the central server. In the learning model upgrading process, we focus more on the wrongly classified data before in the virtual sample and hence to generate sparse learning model parameters. By carefully controlling the size of these groups of samples, we can achieve a tradeoff between privacy and learning performance. Our experimental results show the effectiveness of our proposed scheme by comparing with existing state-of-the-arts.

In stochastic gradient descent, especially for neural network training, there are currently dominating first order methods: not modeling local distance to minimum. This information required for optimal step size is provided by second order methods, however, they have many difficulties, starting with full Hessian having square of dimension number of coefficients. This article proposes a minimal step from successful first order momentum method toward second order: online parabola modelling in just a single direction: normalized $\hat{v}$ from momentum method. It is done by estimating linear trend of gradients $\vec{g}=\nabla F(\vec{\theta})$ in $\hat{v}$ direction: such that $g(\vec{\theta}_\bot+\theta\hat{v})\approx \lambda (\theta -p)$ for $\theta = \vec{\theta}\cdot \hat{v}$, $g= \vec{g}\cdot \hat{v}$, $\vec{\theta}_\bot=\vec{\theta}-\theta\hat{v}$. Using linear regression, $\lambda$, $p$ are MSE estimated by just updating four averages (of $g$, $\theta$, $g\theta$, $\theta^2$) in the considered direction. Exponential moving averages allow here for inexpensive online estimation, weakening contribution of the old gradients. Controlling sign of curvature $\lambda$, we can repel from saddles in contrast to attraction in standard Newton method. In the remaining directions: not considered in second order model, we can simultaneously perform e.g. gradient descent.

Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that in general performing exact inference requires all of the data to be processed at each iteration of the algorithm. For large data sets, the computational cost of MCMC can be prohibitive, which has led to recent developments in scalable Monte Carlo algorithms that have a significantly lower computational cost than standard MCMC. In this paper, we focus on a particular class of scalable Monte Carlo algorithms, stochastic gradient Markov chain Monte Carlo (SGMCMC) which utilises data subsampling techniques to reduce the per-iteration cost of MCMC. We provide an introduction to some popular SGMCMC algorithms and review the supporting theoretical results, as well as comparing the efficiency of SGMCMC algorithms against MCMC on benchmark examples. The supporting R code is available online.

We study the center and median clustering problems for high-dimensional polygonal curves with finite but unbounded complexity. We tackle the computational issue that arises from the high number of dimensions by defining a Johnson-Lindenstrauss projection for polygonal curves. We analyze the resulting error in terms of the Fr\'echet distance, which is a natural dissimilarity measure for curves. Our algorithms for the median clustering achieve sublinear dependency on the number of input curves via subsampling. For the center clustering we utilize Buchin et al. (2019a) algorithm that achieves linear running-time in the number of input curves. We evaluate our results empirically utilizing a fast, CUDA-parallelized variant of the Alt and Godau algorithm for the Fr\'echet distance. Our experiments show that our clustering algorithms have fast and accurate practical implementations that yield meaningful results on real world data from various physical domains.

In the paper, we focus on complexity of C5.0 algorithm for constructing decision tree classifier that is the models for the classification problem from machine learning. In classical case the decision tree is constructed in $O(hd(NM+N \log N))$ running time, where $M$ is a number of classes, $N$ is the size of a training data set, $d$ is a number of attributes of each element, $h$ is a tree height. Firstly, we improved the classical version, the running time of the new version is $O(h\cdot d\cdot N\log N)$. Secondly, we suggest a quantum version of this algorithm, which uses quantum subroutines like the amplitude amplification and the D{\"u}rr-H{\o}yer minimum search algorithms that are based on Grover's algorithm. The running time of the quantum algorithm is $O\big(h\cdot \sqrt{d}\log d \cdot N \log N\big)$ that is better than complexity of the classical algorithm.

Knowledge tracing is the task of modeling each student's mastery of knowledge concepts (KCs) as (s)he engages with a sequence of learning activities. Each student's knowledge is modeled by estimating the performance of the student on the learning activities. It is an important research area for providing a personalized learning platform to students. In recent years, methods based on Recurrent Neural Networks (RNN) such as Deep Knowledge Tracing (DKT) and Dynamic Key-Value Memory Network (DKVMN) outperformed all the traditional methods because of their ability to capture complex representation of human learning. However, these methods face the issue of not generalizing well while dealing with sparse data which is the case with real-world data as students interact with few KCs. In order to address this issue, we develop an approach that identifies the KCs from the student's past activities that are \textit{relevant} to the given KC and predicts his/her mastery based on the relatively few KCs that it picked. Since predictions are made based on relatively few past activities, it handles the data sparsity problem better than the methods based on RNN. For identifying the relevance between the KCs, we propose a self-attention based approach, Self Attentive Knowledge Tracing (SAKT). Extensive experimentation on a variety of real-world dataset shows that our model outperforms the state-of-the-art models for knowledge tracing, improving AUC by 4.43% on average.

In Autonomous Vehicles (AVs), one fundamental pillar is perception, which leverages sensors like cameras and LiDARs (Light Detection and Ranging) to understand the driving environment. Due to its direct impact on road safety, multiple prior efforts have been made to study its the security of perception systems. In contrast to prior work that concentrates on camera-based perception, in this work we perform the first security study of LiDAR-based perception in AV settings, which is highly important but unexplored. We consider LiDAR spoofing attacks as the threat model and set the attack goal as spoofing obstacles close to the front of a victim AV. We find that blindly applying LiDAR spoofing is insufficient to achieve this goal due to the machine learning-based object detection process. Thus, we then explore the possibility of strategically controlling the spoofed attack to fool the machine learning model. We formulate this task as an optimization problem and design modeling methods for the input perturbation function and the objective function. We also identify the inherent limitations of directly solving the problem using optimization and design an algorithm that combines optimization and global sampling, which improves the attack success rates to around 75%. As a case study to understand the attack impact at the AV driving decision level, we construct and evaluate two attack scenarios that may damage road safety and mobility. We also discuss defense directions at the AV system, sensor, and machine learning model levels.

Congestion prediction represents a major priority for traffic management centres around the world to ensure timely incident response handling. The increasing amounts of generated traffic data have been used to train machine learning predictors for traffic, however this is a challenging task due to inter-dependencies of traffic flow both in time and space. Recently, deep learning techniques have shown significant prediction improvements over traditional models, however open questions remain around their applicability, accuracy and parameter tuning. This paper proposes an advanced deep learning framework for simultaneously predicting the traffic flow on a large number of monitoring stations along a highly circulated motorway in Sydney, Australia, including exit and entry loop count stations, and over varying training and prediction time horizons. The spatial and temporal features extracted from the 36.34 million data points are used in various deep learning architectures that exploit their spatial structure (convolutional neuronal networks), their temporal dynamics (recurrent neuronal networks), or both through a hybrid spatio-temporal modelling (CNN-LSTM). We show that our deep learning models consistently outperform traditional methods, and we conduct a comparative analysis of the optimal time horizon of historical data required to predict traffic flow at different time points in the future.