The existence of a universal learning architecture in human cognition is a widely spread conjecture supported by experimental findings from neuroscience. While no low-level implementation can be specified yet, an abstract outline of human perception and learning is believed to entail three basic properties: (a) hierarchical attention and processing, (b) memory-based knowledge representation, and (c) progressive learning and knowledge compaction. We approach the design of such a learning architecture from a system-theoretic viewpoint, developing a closed-loop system with three main components: (i) a multi-resolution analysis pre-processor, (ii) a group-invariant feature extractor, and (iii) a progressive knowledge-based learning module. Multi-resolution feedback loops are used for learning, i.e., for adapting the system parameters to online observations. To design (i) and (ii), we build upon the established theory of wavelet-based multi-resolution analysis and the properties of group convolution operators. Regarding (iii), we introduce a novel learning algorithm that constructs progressively growing knowledge representations in multiple resolutions. The proposed algorithm is an extension of the Online Deterministic Annealing (ODA) algorithm based on annealing optimization, solved using gradient-free stochastic approximation. ODA has inherent robustness and regularization properties and provides a means to progressively increase the complexity of the learning model i.e. the number of the neurons, as needed, through an intuitive bifurcation phenomenon. The proposed multi-resolution approach is hierarchical, progressive, knowledge-based, and interpretable. We illustrate the properties of the proposed architecture in the context of the state-of-the-art learning algorithms and deep learning methods.

Knowledge of Mathematics is essential to understand the data science basics. So if you want to learn Mathematics for Data Science, this article is for you. In this article, you will find the 10 Best Mathematics for Data Science Free Courses. For these courses, You don't need to pay a single buck. Now, without any further ado, let's get started- This is a completely FREE course for beginners and covers data visualization, probability, and many elementary statistics concepts like regression, hypothesis testing, and more.

This hands-on, regression-analysis bootcamp will help you master practical statistical modeling and machine learning in Python. Regression analysis is one of the central aspects of both statistical and machine learning based analysis. This course will teach you regression analysis for both statistical data analysis and machine learning in Python in a practical hands-on manner. It explores the relevant concepts in a practical manner from basic to expert level. This course can help you achieve better grades, give you new analysis tools for your academic career, implement your knowledge in a work setting & make business forecasting related decisions...All of this while exploring the wisdom of an Oxford and Cambridge educated researcher. Most statistics and machine learning courses and books only touch upon the basic aspects of regression analysis.

Hierarchical clustering means creating a tree of clusters by iteratively grouping or separating data points. There are two types of hierarchical clustering named Agglomerative clustering and Divisive clustering. Agglomerative clustering is the bottom-up approach. It merges the two points that are the most similar until all points have been merged into a single cluster. Divisive clustering is the top-down approach.

In this story, I would love to give you a a good idea of how the DINO paper works and what makes it great. I've tried to keep the article simple so that even readers with little prior knowledge can follow along. Traditionally, Vision Transformers (ViT) have not been as attractive as some would expect: They have high computational demands, need more training data, and their features do not exhibit unique properties. With their 2020 paper, "Emerging Properties in Self-Supervised Vision Transformers", Caron et al. aimed to examine why supervised ViT have not yet taken off and if that could be changed by applying self-supervised learning methods to them. This meant that a human would have to create labels for the training data like telling the model that there is a dog in the image.

Good training data is a prerequisite to develop useful Machine Learning applications. However, in many domains existing data sets cannot be shared due to privacy regulations (e.g., from medical studies). This work investigates a simple yet unconventional approach for anonymized data synthesis to enable third parties to benefit from such anonymized data. We explore the feasibility of learning implicitly from visually unrealistic, task-relevant stimuli, which are synthesized by exciting the neurons of a trained deep neural network. As such, neuronal excitation can be used to generate synthetic stimuli. The stimuli data is used to train new classification models. Furthermore, we extend this framework to inhibit representations that are associated with specific individuals. We use sleep monitoring data from both an open and a large closed clinical study, and Electroencephalogram sleep stage classification data, to evaluate whether (1) end-users can create and successfully use customized classification models, and (2) the identity of participants in the study is protected. Extensive comparative empirical investigation shows that different algorithms trained on the stimuli are able to generalize successfully on the same task as the original model. Architectural and algorithmic similarity between new and original models play an important role in performance. For similar architectures, the performance is close to that of using the original data (e.g., Accuracy difference of 0.56%-3.82%, Kappa coefficient difference of 0.02-0.08). Further experiments show that the stimuli can provide state-ofthe-art resilience against adversarial association and membership inference attacks.

The problem of class imbalanced data lies in that the generalization performance of the classifier is deteriorated due to the lack of data of the minority classes. In this paper, we propose a novel minority over-sampling method to augment diversified minority samples by leveraging the rich context of the majority classes as background images. To diversify the minority samples, our key idea is to paste a foreground patch from a minority class to a background image from a majority class having affluent contexts. Our method is simple and can be easily combined with the existing long-tailed recognition methods. We empirically prove the effectiveness of the proposed oversampling method through extensive experiments and ablation studies. Without any architectural changes or complex algorithms, our method achieves state-of-the-art performance on various long-tailed classification benchmarks. Our code will be publicly available at link.

This work examines adaptive distributed learning strategies designed to operate under communication constraints. We consider a network of agents that must solve an online optimization problem from continual observation of streaming data. The agents implement a distributed cooperative strategy where each agent is allowed to perform local exchange of information with its neighbors. In order to cope with communication constraints, the exchanged information must be unavoidably compressed. We propose a diffusion strategy nicknamed as ACTC (Adapt-Compress-Then-Combine), which relies on the following steps: i) an adaptation step where each agent performs an individual stochastic-gradient update with constant step-size; ii) a compression step that leverages a recently introduced class of stochastic compression operators; and iii) a combination step where each agent combines the compressed updates received from its neighbors. The distinguishing elements of this work are as follows. First, we focus on adaptive strategies, where constant (as opposed to diminishing) step-sizes are critical to respond in real time to nonstationary variations. Second, we consider the general class of directed graphs and left-stochastic combination policies, which allow us to enhance the interplay between topology and learning. Third, in contrast with related works that assume strong convexity for all individual agents' cost functions, we require strong convexity only at a network level, a condition satisfied even if a single agent has a strongly-convex cost and the remaining agents have non-convex costs. Fourth, we focus on a diffusion (as opposed to consensus) strategy. Under the demanding setting of compressed information, we establish that the ACTC iterates fluctuate around the desired optimizer, achieving remarkable savings in terms of bits exchanged between neighboring agents.

In this paper, we propose a novel approach for unsupervised domain adaptation, that relates notions of optimal transport, learning probability measures and unsupervised learning. The proposed approach, HOT-DA, is based on a hierarchical formulation of optimal transport, that leverages beyond the geometrical information captured by the ground metric, richer structural information in the source and target domains. The additional information in the labeled source domain is formed instinctively by grouping samples into structures according to their class labels. While exploring hidden structures in the unlabeled target domain is reduced to the problem of learning probability measures through Wasserstein barycenter, which we prove to be equivalent to spectral clustering. Experiments on a toy dataset with controllable complexity and two challenging visual adaptation datasets show the superiority of the proposed approach over the state-of-the-art.

The marginal Bayesian predictive classifiers (mBpc) as opposed to the simultaneous Bayesian predictive classifiers (sBpc), handle each data separately and hence tacitly assumes the independence of the observations. However, due to saturation in learning of generative model parameters, the adverse effect of this false assumption on the accuracy of mBpc tends to wear out in face of increasing amount of training data; guaranteeing the convergence of these two classifiers under de Finetti type of exchangeability. This result however, is far from trivial for the sequences generated under Partition exchangeability (PE), where even umpteen amount of training data is not ruling out the possibility of an unobserved outcome (Wonderland!). We provide a computational scheme that allows the generation of the sequences under PE. Based on that, with controlled increase of the training data, we show the convergence of the sBpc and mBpc. This underlies the use of simpler yet computationally more efficient marginal classifiers instead of simultaneous. We also provide a parameter estimation of the generative model giving rise to the partition exchangeable sequence as well as a testing paradigm for the equality of this parameter across different samples. The package for Bayesian predictive supervised classifications, parameter estimation and hypothesis testing of the Ewens Sampling formula generative model is deposited on CRAN as PEkit package and free available from https://github.com/AmiryousefiLab/PEkit.