Optimisation problems often have multiple conflicting objectives that can be computationally and/or financially expensive. Mono-surrogate Bayesian optimisation (BO) is a popular model-based approach for optimising such black-box functions. It combines objective values via scalarisation and builds a Gaussian process (GP) surrogate of the scalarised values. The location which maximises a cheap-to-query acquisition function is chosen as the next location to expensively evaluate. While BO is an effective strategy, the use of GPs is limiting. Their performance decreases as the problem input dimensionality increases, and their computational complexity scales cubically with the amount of data. To address these limitations, we extend previous work on BO by density-ratio estimation (BORE) to the multi-objective setting. BORE links the computation of the probability of improvement acquisition function to that of probabilistic classification. This enables the use of state-of-the-art classifiers in a BO-like framework. In this work we present MBORE: multi-objective Bayesian optimisation by density-ratio estimation, and compare it to BO across a range of synthetic and real-world benchmarks. We find that MBORE performs as well as or better than BO on a wide variety of problems, and that it outperforms BO on high-dimensional and real-world problems.

Eg; For House price prediction, we first need data about houses such as; square foot, no. of rooms, the house has a garden or not, and so on features. We then need to know the prices of these houses ie; class labels. Now data coming from thousands of houses, their features, and prices, we can now train a supervised machine learning model to predict a new house's price based on past experiences of the model. This algorithm is used to predict the discrete values such as male female, true false, spam not spam, etc. Regression algorithms are used to predict continuous values such as price, salary, age, marks, etc. Another example is Opening emergency hospitals to the maximum prone to accident areas.

This course is about artificial neural networks. Artificial intelligence and machine learning are getting more and more popular nowadays. In the beginning, other techniques such as Support Vector Machines outperformed neural networks, but in the 21st century neural networks again gain popularity. In spite of the slow training procedure, neural networks can be very powerful. In the first part of the course you will learn about the theoretical background of neural networks, later you will learn how to implement them in Python from scratch.

If we are to be struck by an impact event resulting in human extinction, it would most likely occur in the Spring or Fall. If you were to ask 100 people what they believed the greatest risk to human civilization is I would bet the top 3 answers would be nuclear war, global pandemic and global warming/climate change. However, less than 10 years ago a meteor with a diameter of approximately 20 meters and a mass of 10,000 tons exploded 30 km over the city Chelyabinsk in Russia. Although there were no fatalities, the blast was estimated to have resulted in $30 million worth of damages and injured 1,500 people. About 100 years previously, in 1908, a meteor 50–60 meters in size exploded over Siberia with the power of a 12 megaton explosion which destroyed about 2,200 squared kilometers of forest.

Spatial clustering has been widely used for spatial data mining and knowledge discovery. An ideal multivariate spatial clustering should consider both spatial contiguity and aspatial attributes. Existing spatial clustering approaches may face challenges for discovering repeated geographic patterns with spatial contiguity maintained. In this paper, we propose a Spatial Toeplitz Inverse Covariance-Based Clustering (STICC) method that considers both attributes and spatial relationships of geographic objects for multivariate spatial clustering. A subregion is created for each geographic object serving as the basic unit when performing clustering. A Markov random field is then constructed to characterize the attribute dependencies of subregions. Using a spatial consistency strategy, nearby objects are encouraged to belong to the same cluster. To test the performance of the proposed STICC algorithm, we apply it in two use cases. The comparison results with several baseline methods show that the STICC outperforms others significantly in terms of adjusted rand index and macro-F1 score. Join count statistics is also calculated and shows that the spatial contiguity is well preserved by STICC. Such a spatial clustering method may benefit various applications in the fields of geography, remote sensing, transportation, and urban planning, etc.

We introduce HyperMorph, a framework that facilitates efficient hyperparameter tuning in learning-based deformable image registration. Classical registration algorithms perform an iterative pair-wise optimization to compute a deformation field that aligns two images. Recent learning-based approaches leverage large image datasets to learn a function that rapidly estimates a deformation for a given image pair. In both strategies, the accuracy of the resulting spatial correspondences is strongly influenced by the choice of certain hyperparameter values. However, an effective hyperparameter search consumes substantial time and human effort as it often involves training multiple models for different fixed hyperparameter values and may lead to suboptimal registration. We propose an amortized hyperparameter learning strategy to alleviate this burden by learning the impact of hyperparameters on deformation fields. We design a meta network, or hypernetwork, that predicts the parameters of a registration network for input hyperparameters, thereby comprising a single model that generates the optimal deformation field corresponding to given hyperparameter values. This strategy enables fast, high-resolution hyperparameter search at test-time, reducing the inefficiency of traditional approaches while increasing flexibility. We also demonstrate additional benefits of HyperMorph, including enhanced robustness to model initialization and the ability to rapidly identify optimal hyperparameter values specific to a dataset, image contrast, task, or even anatomical region, all without the need to retrain models. We make our code publicly available at http://hypermorph.voxelmorph.net.

Nowadays, detecting anomalous communities in networks is an essential task in research, as it helps discover insights into community-structured networks. Most of the existing methods leverage either information regarding attributes of vertices or the topological structure of communities. In this study, we introduce the Co-Membership-based Generic Anomalous Communities Detection Algorithm (referred as to CMMAC), a novel and generic method that utilizes the information of vertices co-membership in multiple communities. CMMAC is domain-free and almost unaffected by communities' sizes and densities. Specifically, we train a classifier to predict the probability of each vertex in a community being a member of the community. We then rank the communities by the aggregated membership probabilities of each community's vertices. The lowest-ranked communities are considered to be anomalous. Furthermore, we present an algorithm for generating a community-structured random network enabling the infusion of anomalous communities to facilitate research in the field. We utilized it to generate two datasets, composed of thousands of labeled anomaly-infused networks, and published them. We experimented extensively on thousands of simulated, and real-world networks, infused with artificial anomalies. CMMAC outperformed other existing methods in a range of settings. Additionally, we demonstrated that CMMAC can identify abnormal communities in real-world unlabeled networks in different domains, such as Reddit and Wikipedia.

We consider the problem of estimating piecewise regular functions in an online setting, i.e., the data arrive sequentially and at any round our task is to predict the value of the true function at the next revealed point using the available data from past predictions. We propose a suitably modified version of a recently developed online learning algorithm called the sleeping experts aggregation algorithm. We show that this estimator satisfies oracle risk bounds simultaneously for all local regions of the domain. As concrete instantiations of the expert aggregation algorithm proposed here, we study an online mean aggregation and an online linear regression aggregation algorithm where experts correspond to the set of dyadic subrectangles of the domain. The resulting algorithms are near linear time computable in the sample size. We specifically focus on the performance of these online algorithms in the context of estimating piecewise polynomial and bounded variation function classes in the fixed design setup. The simultaneous oracle risk bounds we obtain for these estimators in this context provide new and improved (in certain aspects) guarantees even in the batch setting and are not available for the state of the art batch learning estimators.

GPU, the same code needs 5.2 seconds in total while 4.6 seconds Training classical machine learning models typically means are spent in the Cauchy point subroutine. It can be seen solving an optimization problem. Hence, the design and implementation that while all other parts of the L-BFGS-B algorithm can of solvers for training these models has been be parallelized nicely on a GPU, the inherently sequential and still is an active research topic. While the use of GPUs Cauchy point computation does not and instead, dominates is standard in training deep learning models, most solvers the computation time on the GPU; as a result, the L-BFGS-B for classical machine learning problems still target CPUs.

In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance parameter. By contrast, for Bayesian classification we use a categorical distribution with no mechanism to represent our beliefs about aleatoric uncertainty. Our work shows that explicitly accounting for aleatoric uncertainty significantly improves the performance of Bayesian neural networks. We note that many standard benchmarks, such as CIFAR, have essentially no aleatoric uncertainty. Moreover, we show data augmentation in approximate inference has the effect of softening the likelihood, leading to underconfidence and profoundly misrepresenting our honest beliefs about aleatoric uncertainty. Accordingly, we find that a cold posterior, tempered by a power greater than one, often more honestly reflects our beliefs about aleatoric uncertainty than no tempering -- providing an explicit link between data augmentation and cold posteriors. We show that we can match or exceed the performance of posterior tempering by using a Dirichlet observation model, where we explicitly control the level of aleatoric uncertainty, without any need for tempering.