Current machine learning has made great progress on computer vision and many other fields attributed to the large amount of high-quality training samples, while it does not work very well on genomic data analysis, since they are notoriously known as small data. In our work, we focus on few-shot disease subtype prediction problem, identifying subgroups of similar patients that can guide treatment decisions for a specific individual through training on small data. In fact, doctors and clinicians always address this problem by studying several interrelated clinical variables simultaneously. We attempt to simulate such clinical perspective, and introduce meta learning techniques to develop a new model, which can extract the common experience or knowledge from interrelated clinical tasks and transfer it to help address new tasks. Our new model is built upon a carefully designed meta-learner, called Prototypical Network [35], that is a simple yet effective meta learning machine for few-shot image classification. Observing that gene expression data have specifically high dimensionality and high noise properties compared with image data, we proposed a new extension of it by appending two modules to address these issues. Concretely, we append a feature selection layer to automatically filter out the disease-irrelated genes and incorporate a sample reweighting strategy to adaptively remove noisy data, and meanwhile the extended model is capable of learning from a limited number of training examples and generalize well. Simulations and real gene expression data experiments substantiate the superiority of the proposed method for predicting the subtypes of disease and identifying potential disease-related genes.

Nowadays fairness issues have raised great concerns in decision-making systems. Various fairness notions have been proposed to measure the degree to which an algorithm is unfair. In practice, there frequently exist a certain set of variables we term as fair variables, which are pre-decision covariates such as users' choices. The effects of fair variables are irrelevant in assessing the fairness of the decision support algorithm. We thus define conditional fairness as a more sound fairness metric by conditioning on the fairness variables. Given different prior knowledge of fair variables, we demonstrate that traditional fairness notations, such as demographic parity and equalized odds, are special cases of our conditional fairness notations. Moreover, we propose a Derivable Conditional Fairness Regularizer (DCFR), which can be integrated into any decision-making model, to track the trade-off between precision and fairness of algorithmic decision making. Specifically, an adversarial representation based conditional independence loss is proposed in our DCFR to measure the degree of unfairness. With extensive experiments on three real-world datasets, we demonstrate the advantages of our conditional fairness notation and DCFR.

Wikipedia: "In statistics, Bayesian linear regression is an approach to linear regression in which the statistical analysis is undertaken within the context of Bayesian inference. When the regression model has errors that have a normal distribution, and if a particular form of the prior distribution is assumed, explicit results are available for the posterior probability distributions of the model's parameters." The most common interpretation of Bayes' formula in finance is the diachronic interpretation. This mainly states that over time we learn new information about certain variables or parameters of interest, like the mean return of a time series. Here, H stands for an event, the hypothesis, and D represents the data an experiment or the real world might present.

The scikit-learn library includes tools for data preprocessing and data mining. It is imported in Python via the statement import sklearn. Data can contain all sorts of different values. It is hard to interpret when data take on any range of values. Therefore, we should convert the data into a standard format to make it easier to understand.

Hey guys, I have written my first blog post on how to plot decision boundaries for classification models. Plotting decision boundaries can help immensely in the model selection and hyperparameter tuning process, as it can help detect overfitting or underfitting. I noticed that many online explanations and tutorials explaining overfitting rely on 2D datasets (i.e. Such boundaries can be easily plotted on a 2D plane, but what if your data contains six input features? One can use dimensionality reduction to plot the actual points, but what about the decision boundaries themselves?

One of the most popular Machine Learning algorithms is K-means clustering. It is an unsupervised learning algorithm, meaning that it is used for unlabeled datasets. Imagine that you have several points spread over an n-dimensional space. In order to categorize this data on the basis of their similarity, you will use the K-means clustering algorithm. In this article, we will go through this algorithm in detail.

Attaining prototypical features to represent class distributions is well established in representation learning. However, learning prototypes online from streams of data proves a challenging endeavor as they rapidly become outdated, caused by an ever-changing parameter space in the learning process. Additionally, continual learning does not assume the data stream to be stationary, typically resulting in catastrophic forgetting of previous knowledge. As a first, we introduce a system addressing both problems, where prototypes evolve continually in a shared latent space, enabling learning and prediction at any point in time. In contrast to the major body of work in continual learning, data streams are processed in an online fashion, without additional task-information, and an efficient memory scheme provides robustness to imbalanced data streams. Besides nearest neighbor based prediction, learning is facilitated by a novel objective function, encouraging cluster density about the class prototype and increased inter-class variance. Furthermore, the latent space quality is elevated by pseudo-prototypes in each batch, constituted by replay of exemplars from memory. We generalize the existing paradigms in continual learning to incorporate data incremental learning from data streams by formalizing a two-agent learner-evaluator framework, and obtain state-of-the-art performance by a significant margin on eight benchmarks, including three highly imbalanced data streams. The prevalence of data streams in contemporary applications urges systems to learn in a continual fashion.

The $k$-segmentation of a video stream is used to partition it into $k$ piecewise-linear segments, so that each linear segment has a meaningful interpretation. Such segmentation may be used to summarize large videos using a small set of images, to identify anomalies within segments and change points between segments, and to select critical subsets for training machine learning models. Exact and approximate segmentation methods for $k$-segmentation exist in the literature. Each of these algorithms occupies a different spot in the trade-off between computational complexity and accuracy. A novel heuristic algorithm is proposed in this paper to improve upon existing methods. It is empirically found to provide accuracies competitive with exact methods at a fraction of the computational expense. The new algorithm is inspired by Lloyd's algorithm for K-Means and Lloyd-Max algorithm for scalar quantization, and is called the LM algorithm for convenience. It works by iteratively minimizing a cost function from any given initialisation; the commonly used $L_2$ cost is chosen in this paper. While the greedy minimization makes the algorithm sensitive to initialisation, the ability to converge from any initial guess to a local optimum allows the algorithm to be integrated into other existing algorithms. Three variants of the algorithm are tested over a large number of synthetic datasets, one being a standalone LM implementation, and two others that combine with existing algorithms. One of the latter two -- LM-enhanced-Bottom-Up segmentation -- is found to have the best accuracy and the lowest computational complexity among all algorithms. This variant of LM can provide $k$-segmentations over data sets with up to a million image frames within several seconds.

Open-set recognition and adversarial defense study two key aspects of deep learning that are vital for real-world deployment. The objective of open-set recognition is to identify samples from open-set classes during testing, while adversarial defense aims to defend the network against images with imperceptible adversarial perturbations. In this paper, we show that open-set recognition systems are vulnerable to adversarial attacks. Furthermore, we show that adversarial defense mechanisms trained on known classes do not generalize well to open-set samples. Motivated by this observation, we emphasize the need of an Open-Set Adversarial Defense (OSAD) mechanism. This paper proposes an Open-Set Defense Network (OSDN) as a solution to the OSAD problem. The proposed network uses an encoder with feature-denoising layers coupled with a classifier to learn a noise-free latent feature representation. Two techniques are employed to obtain an informative latent feature space with the objective of improving open-set performance. First, a decoder is used to ensure that clean images can be reconstructed from the obtained latent features. Then, self-supervision is used to ensure that the latent features are informative enough to carry out an auxiliary task. We introduce a testing protocol to evaluate OSAD performance and show the effectiveness of the proposed method in multiple object classification datasets. The implementation code of the proposed method is available at: https://github.com/rshaojimmy/ECCV2020-OSAD.

Clustering techniques have been proved highly suc-cessful for Takagi-Sugeno (T-S) fuzzy model identification. Inparticular, fuzzyc-regression clustering based on type-2 fuzzyset has been shown the remarkable results on non-sparse databut their performance degraded on sparse data. In this paper, aninnovative architecture for fuzzyc-regression model is presentedand a novel student-tdistribution based membership functionis designed for sparse data modelling. To avoid the overfitting,we have adopted a Bayesian approach for incorporating aGaussian prior on the regression coefficients. Additional noveltyof our approach lies in type-reduction where the final output iscomputed using Karnik Mendel algorithm and the consequentparameters of the model are optimized using Stochastic GradientDescent method. As detailed experimentation, the result showsthat proposed approach outperforms on standard datasets incomparison of various state-of-the-art methods.