Algorithms used in the process of machine learning have a number of different functions. They are often used to map data, make sense of large quantities of data, and predict developments over time. There are few algorithms which can conceivably perform all three tasks. One of these is linear regression. This algorithm was originally developed for statistical processing the 19th century.

When an agent encounters a continual stream of new tasks in the lifelong learning setting, it leverages the knowledge it gained from the earlier tasks to help learn the new tasks better. In such a scenario, identifying an efficient knowledge representation becomes a challenging problem. Most research works propose to either store a subset of examples from the past tasks in a replay buffer, dedicate a separate set of parameters to each task or penalize excessive updates over parameters by introducing a regularization term. While existing methods employ the general task-agnostic stochastic gradient descent update rule, we propose a task-aware optimizer that adapts the learning rate based on the relatedness among tasks. We utilize the directions taken by the parameters during the updates by additively accumulating the gradients specific to each task. These task-based accumulated gradients act as a knowledge base that is maintained and updated throughout the stream. We empirically show that our proposed adaptive learning rate not only accounts for catastrophic forgetting but also exhibits knowledge transfer. We also show that our method performs better than several state-of-the-art methods in lifelong learning on complex datasets. Moreover, our method can also be combined with the existing methods and achieve substantial improvement in performance. Lifelong learning (LLL), also known as continual learning, is a setting where an agent continuously learns from data belonging to different tasks (Parisi et al., 2019). Here, the goal is to maximize performance on all the tasks arriving in a stream without replaying the entire datasets from past tasks (Riemer et al., 2018). Approaches proposed in this setting involve investigating the stability-plasticity dilemma (Mermillod et al., 2013) in different ways where stability refers to preventing the forgetting of past knowledge and plasticity refers to accumulating new knowledge by learning new tasks (Mermillod et al., 2013; Delange et al., 2021). 1 Unlike human beings, who can efficiently assess the correctness and applicability of the past knowledge (Chen & Liu, 2018), neural networks and other machine learning models often face various issues in this setting. Whenever data from a new task arrives, these models often tend to forget the previously obtained knowledge due to dependency on the input data distribution, limited capacity, diversity among tasks, etc.

In this paper we present a general framework for estimating regression models subject to a user-defined level of fairness. We enforce fairness as a model selection step in which we choose the value of a ridge penalty to control the effect of sensitive attributes. We then estimate the parameters of the model conditional on the chosen penalty value. Our proposal is mathematically simple, with a solution that is partly in closed form, and produces estimates of the regression coefficients that are intuitive to interpret as a function of the level of fairness. Furthermore, it is easily extended to generalised linear models, kernelised regression models and other penalties; and it can accommodate multiple definitions of fairness. We compare our approach with the regression model from Komiyama et al. (2018), which implements a provably-optimal linear regression model; and with the fair models from Zafar et al. (2019). We evaluate these approaches empirically on six different data sets, and we find that our proposal provides better goodness of fit and better predictive accuracy for the same level of fairness. In addition, we highlight a source of bias in the original experimental evaluation in Komiyama et al. (2018).

Lateral Movement refers to methods by which threat actors gain initial access to a network and then progressively move through said network collecting key data about assets until they reach the ultimate target of their attack. Lateral Movement intrusions have become more intricate with the increasing complexity and interconnected nature of enterprise networks, and require equally sophisticated detection mechanisms to proactively detect such threats in near real-time at enterprise scale. In this paper, the authors propose a novel, lightweight method for Lateral Movement detection using user behavioral analysis and machine learning. Specifically, this paper introduces a novel methodology for cyber domain-specific feature engineering that identifies Lateral Movement behavior on a per-user basis. Furthermore, the engineered features have also been used to develop two supervised machine learning models for Lateral Movement identification that have demonstrably outperformed models previously seen in literature while maintaining robust performance on datasets with high class imbalance. The models and methodology introduced in this paper have also been designed in collaboration with security operators to be relevant and interpretable in order to maximize impact and minimize time to value as a cyber threat detection toolkit. The underlying goal of the paper is to provide a computationally efficient, domain-specific approach to near real-time Lateral Movement detection that is interpretable and robust to enterprise-scale data volumes and class imbalance.

In many real world medical image classification settings we do not have access to samples of all possible disease classes, while a robust system is expected to give high performance in recognizing novel test data. We propose a generalized zero shot learning (GZSL) method that uses self supervised learning (SSL) for: 1) selecting anchor vectors of different disease classes; and 2) training a feature generator. Our approach does not require class attribute vectors which are available for natural images but not for medical images. SSL ensures that the anchor vectors are representative of each class. SSL is also used to generate synthetic features of unseen classes. Using a simpler architecture, our method matches a state of the art SSL based GZSL method for natural images and outperforms all methods for medical images. Our method is adaptable enough to accommodate class attribute vectors when they are available for natural images.

Decentralized optimization with orthogonality constraints is found widely in scientific computing and data science. Since the orthogonality constraints are nonconvex, it is quite challenging to design efficient algorithms. Existing approaches leverage the geometric tools from Riemannian optimization to solve this problem at the cost of high sample and communication complexities. To relieve this difficulty, based on two novel techniques that can waive the orthogonality constraints, we propose a variance-reduced stochastic gradient tracking (VRSGT) algorithm with the convergence rate of $O(1 / k)$ to a stationary point. To the best of our knowledge, VRSGT is the first algorithm for decentralized optimization with orthogonality constraints that reduces both sampling and communication complexities simultaneously. In the numerical experiments, VRSGT has a promising performance in a real-world autonomous driving application.

Recently, decision trees (DT) have been used as an explainable representation of controllers (a.k.a. strategies, policies, schedulers). Although they are often very efficient and produce small and understandable controllers for discrete systems, complex continuous dynamics still pose a challenge. In particular, when the relationships between variables take more complex forms, such as polynomials, they cannot be obtained using the available DT learning procedures. In contrast, support vector machines provide a more powerful representation, capable of discovering many such relationships, but not in an explainable form. Therefore, we suggest to combine the two frameworks in order to obtain an understandable representation over richer, domain-relevant algebraic predicates. We demonstrate and evaluate the proposed method experimentally on established benchmarks.

We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on propagating waves through the graph. However, instead of using a fast Fourier transform (FFT) computation at every node, our proposed approach exploits the Koopman operator framework. Specifically, we show that propagating waves in the graph followed by a local dynamic mode decomposition (DMD) computation at every node is capable of retrieving the eigenvalues and the local eigenvector components of the graph Laplacian, thereby providing local cluster assignments for all nodes. We demonstrate that the DMD computation is more robust than the existing FFT based approach and requires 20 times fewer steps of the wave equation to accurately recover the clustering information and reduces the relative error by orders of magnitude. We demonstrate the decentralized approach on a range of graph clustering problems.

Learning-to-rank, a machine learning technique widely used in information retrieval, has recently been applied to the problem of ligand-based virtual screening, to accelerate the early stages of new drug development. Ranking prediction models learn based on ordinal relationships, making them suitable for integrating assay data from various environments. Existing studies of rank prediction in compound screening have generally used a learning-to-rank method called RankSVM. However, they have not been compared with or validated against the gradient boosting decision tree (GBDT)-based learning-to-rank methods that have gained popularity recently. Furthermore, although the ranking metric called Normalized Discounted Cumulative Gain (NDCG) is widely used in information retrieval, it only determines whether the predictions are better than those of other models. In other words, NDCG is incapable of recognizing when a prediction model produces worse than random results. Nevertheless, NDCG is still used in the performance evaluation of compound screening using learning-to-rank. This study used the GBDT model with ranking loss functions, called lambdarank and lambdaloss, for ligand-based virtual screening; results were compared with existing RankSVM methods and GBDT models using regression. We also proposed a new ranking metric, Normalized Enrichment Discounted Cumulative Gain (NEDCG), which aims to properly evaluate the goodness of ranking predictions. Results showed that the GBDT model with learning-to-rank outperformed existing regression methods using GBDT and RankSVM on diverse datasets. Moreover, NEDCG showed that predictions by regression were comparable to random predictions in multi-assay, multi-family datasets, demonstrating its usefulness for a more direct assessment of compound screening performance.

Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the system's states and inputs. Under a mild marginal mean-square stability assumption, we identify how much data is needed to estimate the unknown bilinear system up to a desired accuracy with high probability. Our sample complexity and statistical error rates are optimal in terms of the trajectory length, the dimensionality of the system and the input size. Our proof technique relies on an application of martingale small-ball condition. This enables us to correctly capture the properties of the problem, specifically our error rates do not deteriorate with increasing instability. Finally, we show that numerical experiments are well-aligned with our theoretical results.