Iterative machine teaching is a method for selecting an optimal teaching example that enables a student to efficiently learn a target concept at each iteration. Existing studies on iterative machine teaching are based on supervised machine learning and assume that there are teachers who know the true answers of all teaching examples. In this study, we consider an unsupervised case where such teachers do not exist; that is, we cannot access the true answer of any teaching example. Students are given a teaching example at each iteration, but there is no guarantee if the corresponding label is correct. Recent studies on crowdsourcing have developed methods for estimating the true answers from crowdsourcing responses. In this study, we apply these to iterative machine teaching for estimating the true labels of teaching examples along with student models that are used for teaching. Our method supports the collaborative learning of students without teachers. The experimental results show that the teaching performance of our method is particularly effective for low-level students in particular.

Prior work on continual learning often operate in a "task-aware" manner, by assuming that the task boundaries and identifies of the data instances are known at all times. While in practice, it is rarely the case that such information are exposed to the methods (i.e., thus called "task-free")--a setting that is relatively underexplored. Recent attempts on task-free continual learning build on previous memory replay methods and focus on developing memory management strategies such that model performance over priorly seen instances can be best retained. In this paper, looking from a complementary angle, we propose a principled approach to "edit" stored examples which aims to carry more updated information from the data stream in the memory. We use gradient updates to edit stored examples so that they are more likely to be forgotten in future updates. Experiments on five benchmark datasets show the proposed method can be seamlessly combined with baselines to significantly improve the performance. Code has been released at https://github.com/INK-USC/GMED.

Anchor-based techniques reduce the computational complexity of spectral clustering algorithms. Although empirical tests have shown promising results, there is currently a lack of theoretical support for the anchoring approach. We define a specific anchor-based algorithm and show that it is amenable to rigorous analysis, as well as being effective in practice. We establish the theoretical consistency of the method in an asymptotic setting where data is sampled from an underlying continuous probability distribution. In particular, we provide sharp asymptotic conditions for the algorithm parameters which ensure that the anchor-based method can recover with high probability disjoint clusters that are mutually separated by a positive distance. We illustrate the performance of the algorithm on synthetic data and explain how the theoretical convergence analysis can be used to inform the practical choice of parameter scalings. We also test the accuracy and efficiency of the algorithm on two large scale real data sets. We find that the algorithm offers clear advantages over standard spectral clustering. We also find that it is competitive with the state-of-the-art LSC method of Chen and Cai (Twenty-Fifth AAAI Conference on Artificial Intelligence, 2011), while having the added benefit of a consistency guarantee.

Global optimization of aerodynamic shapes usually requires a large number of expensive computational fluid dynamics simulations because of the high dimensionality of the design space. One approach to combat this problem is to reduce the design space dimension by obtaining a new representation. This requires a parametric function that compactly and sufficiently describes useful variation in shapes. We propose a deep generative model, B\'ezier-GAN, to parameterize aerodynamic designs by learning from shape variations in an existing database. The resulted new parameterization can accelerate design optimization convergence by improving the representation compactness while maintaining sufficient representation capacity. We use the airfoil design as an example to demonstrate the idea and analyze B\'ezier-GAN's representation capacity and compactness. Results show that B\'ezier-GAN both (1) learns smooth and realistic shape representations for a wide range of airfoils and (2) empirically accelerates optimization convergence by at least two times compared to state-of-the-art parameterization methods.

Gradient descent is a very popular and first-order iterative optimization algorithm for finding a local minimum over a differential function. Similarly, the Normal Equation is another way of doing minimization. It does minimization without restoring to an iterative algorithm. Here, the relationship between the Number of Rooms, and the Price of the House, appears to be Linear. Here, the predictions from the Normal Equation and Linear Equation are the same.

In this article, you'll see top 30 Python libraries for Machine Learning. In this article, you'll see top 30 Python libraries for Machine Learning. Today, Python is one of the most popular programming languages and it has replaced many languages in the industry. There are various reasons for its popularity and one of them is that python has a large collection of libraries. Python is one of the most widely used languages by Data Scientists and Machine Learning experts across the world. Though there is no shortage of alternatives in the form of languages like R, Julia and others, python has steadily and rightfully gained popularity. Similar to the Google Trends shown above(the plot is prepared using matplotlib and pytrends), confidence is visible year over year with python featuring way above its peers in the StackOverflow surveys for 2017 and 2018. These trends/surveys are the consequences of ease of use, shorter learning curve, widespread usage, strong community, large number of libraries covering depth and breadth of a number of research and application areas. The amazing popularity might make one think that python is the gold standard for Machine Learning.

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Typically this requires casting the original deterministic physics-based model into a probabilistic framework where inputs or control variables (CVs) are treated as random variables with probability distributions derived from available experimental data, manufacturing constraints, design criteria, expert judgment, and/or other domain knowledge (e.g., see [1]). Running the physics-based model with CVs sampled according to these distributions yields corresponding realizations of the system response as characterized by quantities of interest (QoIs). Analysis of the uncertainty propagation from the CVs to the QoIs informs decision-making, e.g., it informs engineering decisions aimed at improving the quality and reliability of designed products and helps identify potential risks at early stages in the design and manufacturing process. Quantitatively assessing uncertainty propagation presents a fundamental challenge due to the computational cost of the underlying physics-based model. Even for a low number of CVs and QoIs, uncertainty quantification (UQ) for, e.g., accelerating the simulation-aided design of multiscale systems and data-centric engineering tasks more generally ([2]), requires a large number of repeated observations of QoIs to achieve a high degree of confidence in such an analysis. The sampling cost is further exacerbated in real-world applications where distributions on QoIs are typically non-Gaussian, skewed, and/or mutually correlated, and therefore need to be characterized by their full probability density function (PDF) rather than through summary statistics such as mean and variance. The computational cost of nonparametric methods to estimate these densities can become prohibitively high when using a fully-featured physics-based model to compute each sample. One approach to alleviate the computational burden is to derive a cheaper-to-compute surrogate for the physicsbased model's response enabling much faster generation of output data and thus overcoming computational bottlenecks.

In recent years, Deep Reinforcement Learning (DRL) algorithms have achieved state-of-the-art performance in many challenging strategy games. Because these games have complicated rules, an action sampled from the full discrete action space will typically be invalid. The usual approach to deal with this problem in policy gradient algorithms is to "mask out" invalid actions and just sample from the set of valid actions. The implications of this process, however, remain under-investigated. In this paper, we show that the standard working mechanism of invalid action masking corresponds to valid policy gradient updates. More interestingly, it works by applying a state-dependent differentiable function during the calculation of action probability distribution. Additionally, we show its critical importance to the performance of policy gradient algorithms. Specifically, our experiments show that invalid action masking scales well when the space of invalid actions is large, while the common approach of giving negative rewards for invalid actions will fail. Finally, we provide further insights by evaluating different action masking regimes, such as removing masking after an agent has been trained using masking.

We study the Extended Kalman Filter in constant dynamics, offering a bayesian perspective of stochastic optimization. We obtain high probability bounds on the cumulative excess risk in an unconstrained setting. In order to avoid any projection step we propose a two-phase analysis. First, for linear and logistic regressions, we prove that the algorithm enters a local phase where the estimate stays in a small region around the optimum. We provide explicit bounds with high probability on this convergence time. Second, for generalized linear regressions, we provide a martingale analysis of the excess risk in the local phase, improving existing ones in bounded stochastic optimization. The EKF appears as a parameter-free online algorithm with O(d^2) cost per iteration that optimally solves some unconstrained optimization problems.