One-hot labels do not represent soft decision boundaries among concepts, and hence, models trained on them are prone to overfitting. Using soft labels as targets provide regularization, but different soft labels might be optimal at different stages of optimization. Also, training with fixed labels in the presence of noisy annotations leads to worse generalization. To address these limitations, we propose a framework, where we treat the labels as learnable parameters, and optimize them along with model parameters. The learned labels continuously adapt themselves to the model's state, thereby providing dynamic regularization. When applied to the task of supervised image-classification, our method leads to consistent gains across different datasets and architectures. For instance, dynamically learned labels improve ResNet18 by 2.1% on CIFAR100. When applied to dataset containing noisy labels, the learned labels correct the annotation mistakes, and improves over state-of-the-art by a significant margin. Finally, we show that learned labels capture semantic relationship between classes, and thereby improve teacher models for the downstream task of distillation.

We provide an Information-Geometric formulation of Classical Mechanics on the Riemannian manifold of probability distributions, which is an affine manifold endowed with a dually-flat connection. In a non-parametric formalism, we consider the full set of positive probability functions on a finite sample space, and we provide a specific expression for the tangent and cotangent spaces over the statistical manifold, in terms of a Hilbert bundle structure that we call the Statistical Bundle. In this setting, we compute velocities and accelerations of a one-dimensional statistical model using the canonical dual pair of parallel transports and define a coherent formalism for Lagrangian and Hamiltonian mechanics on the bundle. Finally, in a series of examples, we show how our formalism provides a consistent framework for accelerated natural gradient dynamics on the probability simplex, paving the way for direct applications in optimization, game theory and neural networks.

Continual learning from streaming data sources becomes more and more popular due to the increasing number of online tools and systems. Dealing with dynamic and everlasting problems poses new challenges for which traditional batch-based offline algorithms turn out to be insufficient in terms of computational time and predictive performance. One of the most crucial limitations is that we cannot assume having access to a finite and complete data set - we always have to be ready for new data that may complement our model. This poses a critical problem of providing labels for potentially unbounded streams. In the real world, we are forced to deal with very strict budget limitations, therefore, we will most likely face the scarcity of annotated instances, which are essential in supervised learning. In our work, we emphasize this problem and propose a novel instance exploitation technique. We show that when: (i) data is characterized by temporary non-stationary concepts, and (ii) there are very few labels spanned across a long time horizon, it is actually better to risk overfitting and adapt models more aggressively by exploiting the only labeled instances we have, instead of sticking to a standard learning mode and suffering from severe underfitting. We present different strategies and configurations for our methods, as well as an ensemble algorithm that attempts to maintain a sweet spot between risky and normal adaptation. Finally, we conduct a complex in-depth comparative analysis of our methods, using state-of-the-art streaming algorithms relevant to the given problem.

In this paper, we propose a novel framework for Deep Clustering and Representation Learning (DCRL) that preserves the geometric structure of data. In the proposed DCRL framework, manifold clustering is done in the latent space guided by a clustering loss. To overcome the problem that clustering-oriented losses may deteriorate the geometric structure of embeddings in the latent space, an isometric loss is proposed for preserving intra-manifold structure locally and a ranking loss for inter-manifold structure globally. Experimental results on various datasets show that the DCRL framework leads to performances comparable to current state-of-the-art deep clustering algorithms, yet exhibits superior performance for downstream tasks. Our results also demonstrate the importance and effectiveness of the proposed losses in preserving geometric structure in terms of visualization and performance metrics. Clustering, a fundamental tool for data analysis and visualization, has been an essential research topic in data science and machine learning. Conventional clustering algorithms such as K -Means (MacQueen, 1965), Gaussian Mixture Models (GMM) (Bishop, 2006), and spectral clustering (Shi & Malik, 2000) perform clustering based on distance or similarity. However, handcrafted distance or similarity measures are rarely reliable for large-scale high-dimensional data, making it increasingly challenging to achieve effective clustering.

We all are well aware of the capability of python libraries in machine learning, but you can also manipulate the image properties with the help of the matplotlib library. We will see how we can easily transform and manipulate image properties. We have imported the required libraries, Also cv2 is used to read and manipulate the image. Make sure that the image you want to manipulate lies in the same folder. As we know, image properties are generally in 3-dimension, it is very clear with the output we got (350, 525, 3).

This intriguing double descent behavior also occurs as a function of training epochs, and has been conjectured to arise because training epochs control the model complexity. In this paper, we show that such epoch-wise double descent arises for a different reason: It is caused by a superposition of two or more bias-variance tradeoffs that arise because different parts of the network are learned at different epochs, and eliminating this by proper scaling of stepsizes can significantly improve the early stopping performance. We show this analytically for i) linear regression, where differently scaled features give rise to a superposition of bias-variance tradeoffs, and for ii) a two-layer neural network, where the first and second layer each govern a bias-variance tradeoff. Inspired by this theory, we study two standard convolutional networks empirically, and show that eliminating epoch-wise double descent through adjusting stepsizes of different layers improves the early stopping performance significantly.

In the existing research of mammogram image classification, either clinical data or image features of a specific type is considered along with the supervised classifiers such as Neural Network (NN) and Support Vector Machine (SVM). This paper considers automated classification of breast tissue type as benign or malignant using Weighted Feature Support Vector Machine (WFSVM) through constructing the precomputed kernel function by assigning more weight to relevant features using the principle of maximizing deviations. Initially, MIAS dataset of mammogram images is divided into training and test set, then the preprocessing techniques such as noise removal and background removal are applied to the input images and the Region of Interest (ROI) is identified. The statistical features and texture features are extracted from the ROI and the clinical features are obtained directly from the dataset. The extracted features of the training dataset are used to construct the weighted features and precomputed linear kernel for training the WFSVM, from which the training model file is created. Using this model file the kernel matrix of test samples is classified as benign or malignant. This analysis shows that the texture features have resulted in better accuracy than the other features with WFSVM and SVM. However, the number of support vectors created in WFSVM is less than the SVM classifier.

Synchronous stochastic gradient descent (SGD) is the most common method used for distributed training of deep learning models. In this algorithm, each worker shares its local gradients with others and updates the parameters using the average gradients of all workers. Although distributed training reduces the computation time, the communication overhead associated with the gradient exchange forms a scalability bottleneck for the algorithm. There are many compression techniques proposed to reduce the number of gradients that needs to be communicated. However, compressing the gradients introduces yet another overhead to the problem. In this work, we study several compression schemes and identify how three key parameters affect the performance. We also provide a set of insights on how to increase performance and introduce a simple sparsification scheme, random-block sparsification, that reduces communication while keeping the performance close to standard SGD.

This paper describes a new win-rate based bid shading algorithm (WR) that does not rely on the minimum-bid-to-win feedback from a Sell-Side Platform (SSP). The method uses a modified logistic regression to predict the profit from each possible shaded bid price. The function form allows fast maximization at run-time, a key requirement for Real-Time Bidding (RTB) systems. We report production results from this method along with several other algorithms. We found that bid shading, in general, can deliver significant value to advertisers, reducing price per impression to about 55% of the unshaded cost. Further, the particular approach described in this paper captures 7% more profit for advertisers, than do benchmark methods of just bidding the most probable winning price. We also report 4.3% higher surplus than an industry Sell-Side Platform shading service. Furthermore, we observed 3% - 7% lower eCPM, eCPC and eCPA when the algorithm was integrated with budget controllers. We attribute the gains above as being mainly due to the explicit maximization of the surplus function, and note that other algorithms can take advantage of this same approach.

Sequential learning systems are used in a wide variety of problems from decision making to optimization, where they provide a 'belief' (opinion) to nature, and then update this belief based on the feedback (result) to minimize (or maximize) some cost or loss (conversely, utility or gain). The goal is to reach an objective by exploiting the temporal relation inherent to the nature's feedback (state). By exploiting this relation, specific learning systems can be designed that perform asymptotically optimal for various applications. However, if the framework of the problem is not stationary, i.e., the nature's state sometimes changes arbitrarily, the past cumulative belief revision done by the system may become useless and the system may fail if it lacks adaptivity. While this adaptivity can be directly implemented in specific cases (e.g., convex optimization), it is mostly not straightforward for general learning tasks. To this end, we propose an efficient optimal mixture framework for general sequential learning systems, which we call the recursive experts for dynamic environments. For this purpose, we design hyper-experts that incorporate the learning systems at our disposal and recursively merge in a specific way to achieve minimax optimal regret bounds up to constant factors. The multiplicative increases in computational complexity from the initial system to our adaptive system are only logarithmic-in-time factors.