Network topology identification (TI) is an essential function for distributed energy resources management systems (DERMS) to organize and operate widespread distributed energy resources (DERs). In this paper, discriminant analysis (DA) is deployed to develop a network TI function that relies only on the measurements available to DERMS. The propounded method is able to identify the network switching configuration, as well as the status of protective devices. Following, to improve the TI resiliency against the interruption of communication channels, a quadratic programming optimization approach is proposed to recover the missing signals. By deploying the propounded data recovery approach and Bayes' theorem together, a benchmark is developed afterward to identify anomalous measurements. This benchmark can make the TI function resilient against cyber-attacks. Having a low computational burden, this approach is fast-track and can be applied in real-time applications. Sensitivity analysis is performed to assess the contribution of different measurements and the impact of the system load type and loading level on the performance of the proposed approach.

In this paper, we propose a new {\it \underline{R}ecursive} {\it \underline{I}mportance} {\it \underline{S}ketching} algorithm for {\it \underline{R}ank} constrained least squares {\it \underline{O}ptimization} (RISRO). As its name suggests, the algorithm is based on a new sketching framework, recursive importance sketching. Several existing algorithms in the literature can be reinterpreted under the new sketching framework and RISRO offers clear advantages over them. RISRO is easy to implement and computationally efficient, where the core procedure in each iteration is only solving a dimension reduced least squares problem. Different from numerous existing algorithms with locally geometric convergence rate, we establish the local quadratic-linear and quadratic rate of convergence for RISRO under some mild conditions. In addition, we discover a deep connection of RISRO to Riemannian manifold optimization on fixed rank matrices. The effectiveness of RISRO is demonstrated in two applications in machine learning and statistics: low-rank matrix trace regression and phase retrieval. Simulation studies demonstrate the superior numerical performance of RISRO.

Preview this course - GET COUPON CODE Have you ever thought about what would happen if you combined the power of machine learning and artificial intelligence with financial engineering? Today, you can stop imagining, and start doing. This course will teach you the core fundamentals of financial engineering, with a machine learning twist. We will cover must-know topics in financial engineering, such as: Exploratory data analysis, significance testing, correlations, alpha and beta Time series analysis, simple moving average, exponentially-weighted moving average Holt-Winters exponential smoothing model Efficient Market Hypothesis Random Walk Hypothesis Time series forecasting ("stock price prediction") Modern portfolio theory Efficient frontier / Markowitz bullet Mean-variance optimization Maximizing the Sharpe ratio Convex optimization with Linear Programming and Quadratic Programming Capital Asset Pricing Model (CAPM) Algorithmic trading (VIP only) Statistical Factor Models (VIP only) Regime Detection with Hidden Markov Models (VIP only) In addition, we will look at various non-traditional techniques which stem purely from the field of machine learning and artificial intelligence, such as: Classification models Unsupervised learning Reinforcement learning and Q-learning ***VIP-only sections (get it while it lasts!) You will learn exactly why their methodology is fundamentally flawed and why their results are complete nonsense.

When working on a machine learning project, you need to follow a series of steps until you reach your goal. One of the steps you have to perform is hyperparameter optimization on your selected model. This task always comes after the model selection process where you choose the model that is performing better than other models. Before I define hyperparameter optimization, you need to understand what a hyperparameter is. In short, hyperparameters are different parameter values that are used to control the learning process and have a significant effect on the performance of machine learning models. An example of hyperparameters in the Random Forest algorithm is the number of estimators (n_estimators), maximum depth (max_depth), and criterion. These parameters are tunable and can directly affect how well a model trains. So then hyperparameter optimization is the process of finding the right combination of hyperparameter values to achieve maximum performance on the data in a reasonable amount of time.

Ill-managed intersections are the primary reasons behind the increasing traffic problem in urban areas, leading to nonoptimal traffic-flow and unnecessary deadlocks. In this paper, we propose an automated intersection management system that extracts data from a well-defined grid of sensors and optimizes traffic flow by controlling traffic signals. The data extraction mechanism is independent of the optimization algorithm and this paper primarily emphasizes the later one. We have used MiniZinc modeling language to define our system as a constraint satisfaction problem which can be solved using any off-the-shelf solver. The proposed system performs much better than the systems currently in use. Our system reduces the mean waiting time and standard deviation of the waiting time of vehicles and avoids deadlocks.

With growing awareness of societal impact of artificial intelligence, fairness has become an important aspect of machine learning algorithms. The issue is that human biases towards certain groups of population, defined by sensitive features like race and gender, are introduced to the training data through data collection and labeling. Two important directions of fairness ensuring research have focused on (i) instance weighting in order to decrease the impact of more biased instances and (ii) adversarial training in order to construct data representations informative of the target variable, but uninformative of the sensitive attributes. In this paper we propose a Fair Adversarial Instance Re-weighting (FAIR) method, which uses adversarial training to learn instance weighting function that ensures fair predictions. Merging the two paradigms, it inherits desirable properties from both -- interpretability of reweighting and end-to-end trainability of adversarial training. We propose four different variants of the method and, among other things, demonstrate how the method can be cast in a fully probabilistic framework. Additionally, theoretical analysis of FAIR models' properties have been studied extensively. We compare FAIR models to 7 other related and state-of-the-art models and demonstrate that FAIR is able to achieve a better trade-off between accuracy and unfairness. To the best of our knowledge, this is the first model that merges reweighting and adversarial approaches by means of a weighting function that can provide interpretable information about fairness of individual instances.

When the human-robot interactions become ubiquitous, the environment surrounding these interactions will have significant impact on the safety and comfort of the human and the effectiveness and efficiency of the robot. Although most robots are designed to work in the spaces created for humans, many environments, such as living rooms and offices, can be and should be redesigned to enhance and improve human-robot collaboration and interactions. This work uses autonomous wheelchair as an example and investigates the computational design in the human-robot coexistence spaces. Given the room size and the objects $O$ in the room, the proposed framework computes the optimal layouts of $O$ that satisfy both human preferences and navigation constraints of the wheelchair. The key enabling technique is a motion planner that can efficiently evaluate hundreds of similar motion planning problems. Our implementation shows that the proposed framework can produce a design around three to five minutes on average comparing to 10 to 20 minutes without the proposed motion planner. Our results also show that the proposed method produces reasonable designs even for tight spaces and for users with different preferences.

Learned optimizers are algorithms that can be trained to solve optimization problems. Although learned optimizers can outperform baseline optimizers in restricted settings, the ML research community understands remarkably little about their inner workings or why they work as well as they do. In a paper currently under review for ICLR 2021, a Google Brain research team attempts to shed some light on the matter. The researchers explain that optimization algorithms can be considered the basis of modern machine learning. A popular research area in recent years has focused on learning optimization algorithms by directly parameterizing and training an optimizer on a distribution of tasks. Research on learned optimizers aims to replace the baseline "hand-designed" optimizers with a parametric optimizer trained on a set of tasks, which can then be applied more generally.

Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems in the design of optimization algorithms for bilevel optimization is the efficient computation of the gradient of the upper-level objective (hypergradient). In this work, we study stochastic approximation schemes for the hypergradient, which are important when the lower-level problem is empirical risk minimization on a large dataset. We provide iteration complexity bounds for the mean square error of the hypergradient approximation, under the assumption that the lower-level problem is accessible only through a stochastic mapping which is a contraction in expectation. Preliminary numerical experiments support our theoretical analysis.

Convex optimizers have known many applications as differentiable layers within deep neural architectures. One application of these convex layers is to project points into a convex set. However, both forward and backward passes of these convex layers are significantly more expensive to compute than those of a typical neural network. We investigate in this paper whether an inexact, but cheaper projection, can drive a descent algorithm to an optimum. Specifically, we propose an interpolation-based projection that is computationally cheap and easy to compute given a convex, domain defining, function. We then propose an optimization algorithm that follows the gradient of the composition of the objective and the projection and prove its convergence for linear objectives and arbitrary convex and Lipschitz domain defining inequality constraints. In addition to the theoretical contributions, we demonstrate empirically the practical interest of the interpolation projection when used in conjunction with neural networks in a reinforcement learning and a supervised learning setting.