We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a desired accuracy in mean-squared error. We provide the first sample and computationally efficient algorithm for this problem in any fixed dimension. Our algorithm relies on a simple iterative merging approach, which is novel in the multidimensional setting. Our experimental evaluation on both synthetic and real datasets shows that our algorithm is competitive and in some cases outperforms state-of-the-art heuristics. Code of our implementation is available at \url{https://github.com/avoloshinov/multidimensional-segmented-regression}.

Graph clustering has been studied extensively on both plain graphs and attributed graphs. However, all these methods need to partition the whole graph to find cluster structures. Sometimes, based on domain knowledge, people may have information about a specific target region in the graph and only want to find a single cluster concentrated on this local region. Such a task is called local clustering. In contrast to global clustering, local clustering aims to find only one cluster that is concentrating on the given seed vertex (and also on the designated attributes for attributed graphs). Currently, very few methods can deal with this kind of task. To this end, we propose two quality measures for a local cluster: Graph Unimodality (GU) and Attribute Unimodality (AU). The former measures the homogeneity of the graph structure while the latter measures the homogeneity of the subspace that is composed of the designated attributes. We call their linear combination as Compactness. Further, we propose LOCLU to optimize the Compactness score. The local cluster detected by LOCLU concentrates on the region of interest, provides efficient information flow in the graph and exhibits a unimodal data distribution in the subspace of the designated attributes.

Intensive Care Unit Electronic Health Records (ICU EHRs) store multimodal data about patients including clinical notes, sparse and irregularly sampled physiological time series, lab results, and more. To date, most methods designed to learn predictive models from ICU EHR data have focused on a single modality. In this paper, we leverage the recently proposed interpolation-prediction deep learning architecture(Shukla and Marlin 2019) as a basis for exploring how physiological time series data and clinical notes can be integrated into a unified mortality prediction model. We study both early and late fusion approaches and demonstrate how the relative predictive value of clinical text and physiological data change over time. Our results show that a late fusion approach can provide a statistically significant improvement in mortality prediction performance over using individual modalities in isolation.

We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix completion problem is transformed into a problem of solving a system of nonlinear equations, and the alternative direction method is then used to solve the nonlinear equations. In addition, the algorithm is highly parallelizable and suitable for large scale problems. Theoretically, we characterize the sufficient conditions for when $L_*$ can be approximated by a low rank approximation of the observed $M_*$. And under proper assumptions, it is shown that the algorithm converges to the true solution linearly. Numerical simulations show that the simple method works as expected and is comparable with state-of-the-art methods.

Federated learning is a decentralized machine learning technique that evokes widespread attention in both the research field and the real-world market. However, the current privacy-preserving federated learning scheme only provides a secure way for the users to contribute their private data but never leaves a way to withdraw the contribution to model update. Such an irreversible setting potentially breaks the regulations about data protection and increases the risk of data extraction. To resolve the problem, this paper describes a novel concept for federated learning, called memorization elimination. Based on the concept, we propose \sysname, a federated learning framework that allows the user to eliminate the memorization of its private data in the trained model. Specifically, each user in \sysname is deployed with a trainable dummy gradient generator. After steps of training, the generator can produce dummy gradients to stimulate the neurons of a machine learning model to eliminate the memorization of the specific data. Also, we prove that the additional memorization elimination service of \sysname does not break the common procedure of federated learning or lower its security.

We introduce a cluster evaluation technique called Tree Index. Our Tree Index algorithm aims at describing the structural information of the clustering rather than the quantitative format of cluster-quality indexes (where the representation power of clustering is some cumulative error similar to vector quantization). Our Tree Index is finding margins amongst clusters for easy learning without the complications of Minimum Description Length. Our Tree Index produces a decision tree from the clustered data set, using the cluster identifiers as labels. It combines the entropy of each leaf with their depth. Intuitively, a shorter tree with pure leaves generalizes the data well (the clusters are easy to learn because they are well separated). So, the labels are meaningful clusters. If the clustering algorithm does not separate well, trees learned from their results will be large and too detailed. We show that, on the clustering results (obtained by various techniques) on a brain dataset, Tree Index discriminates between reasonable and non-sensible clusters. We confirm the effectiveness of Tree Index through graphical visualizations. Tree Index evaluates the sensible solutions higher than the non-sensible solutions while existing cluster-quality indexes fail to do so.

Spatial trajectories are ubiquitous and complex signals. Their analysis is crucial in many research fields, from urban planning to neuroscience. Several approaches have been proposed to cluster trajectories. They rely on hand-crafted features, which struggle to capture the spatio-temporal complexity of the signal, or on Artificial Neural Networks (ANNs) which can be more efficient but less interpretable. In this paper we present a novel ANN architecture designed to capture the spatio-temporal patterns characteristic of a set of trajectories, while taking into account the demographics of the navigators. Hence, our model extracts markers linked to both behaviour and demographics. We propose a composite signal analyser (CompSNN) combining three simple ANN modules. Each of these modules uses different signal representations of the trajectory while remaining interpretable. Our CompSNN performs significantly better than its modules taken in isolation and allows to visualise which parts of the signal were most useful to discriminate the trajectories.

With the increase in scale and complexity of ICT systems, their operation increasingly requires automatic recovery from failures. Although it has become possible to automatically detect anomalies and analyze root causes of failures with current methods, making decisions on what commands should be executed to recover from failures still depends on manual operation, which is quite time-consuming. Toward automatic recovery, we propose a method of estimating recovery commands by using Seq2Seq, a neural network model. This model learns complex relationships between logs obtained from equipment and recovery commands that operators executed in the past. When a new failure occurs, our method estimates plausible commands that recover from the failure on the basis of collected logs. We conducted experiments using a synthetic dataset and realistic OpenStack dataset, demonstrating that our method can estimate recovery commands with high accuracy.

Health monitoring is important for maintaining reliable information and communications technology (ICT) systems. Anomaly detection methods based on machine learning, which train a model for describing "normality" are promising for monitoring the state of ICT systems. However, these methods cannot be used when the type of monitored log data changes from that of training data due to the replacement of certain equipment. Therefore, such methods may dismiss an anomaly that appears when log data changes. To solve this problem, we propose an ICT-systems-monitoring method with deep learning models divided based on the correlation of log data. We also propose an algorithm for extracting the correlations of log data from a deep learning model and separating log data based on the correlation. When some of the log data changes, our method can continue health monitoring with the divided models which are not affected by changes in the log data. We present the results from experiments involving benchmark data and real log data, which indicate that our method using divided models does not decrease anomaly detection accuracy and a model for anomaly detection can be divided to continue monitoring a network state even if some the log data change.

Object frequency in the real world often follows a power law, leading to a mismatch between datasets with long-tailed class distributions seen by a machine learning model and our expectation of the model to perform well on all classes. We analyze this mismatch from a domain adaptation point of view. First of all, we connect existing class-balanced methods for long-tailed classification to target shift, a well-studied scenario in domain adaptation. The connection reveals that these methods implicitly assume that the training data and test data share the same class-conditioned distribution, which does not hold in general and especially for the tail classes. While a head class could contain abundant and diverse training examples that well represent the expected data at inference time, the tail classes are often short of representative training data. To this end, we propose to augment the classic class-balanced learning by explicitly estimating the differences between the class-conditioned distributions with a meta-learning approach. We validate our approach with six benchmark datasets and three loss functions.