The clustering algorithms that view each object data as a single sample drawn from a certain distribution, Gaussian distribution, for example, has been a hot topic for decades. Many clustering algorithms: such as k-means and spectral clustering are proposed based on the single sample assumption. However, in real life, each input object can usually be the multiple samples drawn from a certain hidden distribution. The traditional clustering algorithms cannot handle such a situation. This calls for the multiple sample clustering algorithm. But the traditional multiple sample clustering algorithms can only handle scalar samples or samples from Gaussian distribution. This constrains the application field of multiple sample clustering algorithms. In this paper, we purpose a general framework for multiple sample clustering. Various algorithms can be generated by this framework. We apply two specific cases of this framework: Wasserstein distance version and Bhattacharyya distance version on both synthetic data and stock price data. The simulation results show that the sufficient statistic can greatly improve the clustering accuracy and stability.

This paper proposes SplitSGD, a new stochastic optimization algorithm with a dynamic learning rate selection rule. This procedure decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is detected, that is, the iterates are likely to bounce around a vicinity of a local minimum. The detection is performed by splitting the single thread into two and using the inner products of the gradients from the two threads as a measure of stationarity. This learning rate selection is provably valid, robust to initial parameters, easy-to-implement, and essentially does not incur additional computational cost. Finally, we illustrate the robust convergence properties of SplitSGD through extensive experiments.

We investigate the use of a non-parametric independence measure, the Hilbert-Schmidt Independence Criterion (HSIC), as a loss-function for learning robust regression and classification models. This loss-function encourages learning models where the distribution of the residuals between the label and the model-prediction is statistically independent of the distribution of the instances themselves. This loss-function was first proposed by Mooij et al. [2009] in the context of learning causal graphs. We adapt it to the task of robust learning for unsupervised covariate shift: learning on a source domain without access to any instances or labels from the unknown target domain. We prove that the proposed loss is expected to generalize to a class of target domains described in terms of the complexity of their density ratio function with respect to the source domain. Experiments on tasks of unsupervised covariate shift demonstrate that models learned with the proposed loss-function outperform several baseline methods.

Sports competitions are widely researched in computer and social science, with the goal of understanding how players act under uncertainty. While there is an abundance of computational work on player metrics prediction based on past performance, very few attempts to incorporate out-of-game signals have been made. Specifically, it was previously unclear whether linguistic signals gathered from players' interviews can add information which does not appear in performance metrics. To bridge that gap, we define text classification tasks of predicting deviations from mean in NBA players' in-game actions, which are associated with strategic choices, player behavior and risk, using their choice of language prior to the game. We collected a dataset of transcripts from key NBA players' pre-game interviews and their in-game performance metrics, totaling in 5,226 interview-metric pairs. We design neural models for players' action prediction based on increasingly more complex aspects of the language signals in their open-ended interviews. Our models can make their predictions based on the textual signal alone, or on a combination with signals from past-performance metrics. Our text-based models outperform strong baselines trained on performance metrics only, demonstrating the importance of language usage for action prediction. Moreover, the models that employ both textual input and past-performance metrics produced the best results. Finally, as neural networks are notoriously difficult to interpret, we propose a method for gaining further insight into what our models have learned. Particularly, we present an LDA-based analysis, where we interpret model predictions in terms of correlated topics. We find that our best performing textual model is most associated with topics that are intuitively related to each prediction task and that better models yield higher correlation with more informative topics.

Are you trying to predict time series but don't know where to start? This blog post will provide a comparison of the most prominent techniques and show you how to implement them. Time Series prediction can be used in a number of business areas. You can think of a number of areas and questions. Generally, a prediction problem involves using past observations to predict or forecast one or more possible future observations. The goal is to guess about what might happen in the future. Knowing the future can impact our decisions today so we have a great interest in predicting it.

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"Any AI smart enough to pass a Turing test is smart enough to know to fail it." Suppose you are working on a high-impact yet challenging problem of malware classification. You have a large dataset at your disposal and are able to train a machine learning classifier with an accuracy of 98%. While suppressing your excitement, you convince the team to deploy the model, as who would resist a model with such an amazing performance? Quite disappointingly, the model fails to detect threats in the real world!?

In this post we will talk about applying gradient descent on \(m\) training examples. Now the question is how we can define what gradient descent is? A gradient descent is an efficient optimization algorithm that attempts to find a global minimum of a function. It also enables a model to calculate the gradient or direction that the model should take to reduce errors (differences between actual \(y\) and predicted \(\hat{y}\)). Now let's remind ourselves what the cost function is?

Description: A down-to-earth, shy but confident take on machine learning techniques that you can put to work today.

A salient approach to interpretable machine learning is to restrict modeling to simple and hence understandable models. In the Bayesian framework, this can be pursued by restricting the model structure and prior to favor interpretable models. Fundamentally, however, interpretability is about users' preferences, not the data generation mechanism: it is more natural to formulate interpretability as a utility function. In this work, we propose an interpretability utility, which explicates the trade-off between explanation fidelity and interpretability in the Bayesian framework. The method consists of two steps.