In this work, we study an optimizer, Grad-Avg to optimize error functions. We establish the convergence of the sequence of iterates of Grad-Avg mathematically to a minimizer (under boundedness assumption). We apply Grad-Avg along with some of the popular optimizers on regression as well as classification tasks. In regression tasks, it is observed that the behaviour of Grad-Avg is almost identical with Stochastic Gradient Descent (SGD). We present a mathematical justification of this fact. In case of classification tasks, it is observed that the performance of Grad-Avg can be enhanced by suitably scaling the parameters. Experimental results demonstrate that Grad-Avg converges faster than the other state-of-the-art optimizers for the classification task on two benchmark datasets.

Our little journey to machine learning with R continues! Today's topic is logistic regression – as an introduction to machine learning classification tasks. We'll cover data preparation, modeling, and evaluation of the well-known Titanic dataset. That's it for the introduction section – we have many things to cover, so let's jump right to it. Logistic regression is a great introductory algorithm for binary classification (two class values) borrowed from the field of statistics.

This tutorial covers the entire ML process, from data ingestion, pre-processing, model training, hyper-parameter fitting, predicting and storing the model for later use. Let's see the whole picture Recreating the entire experiment without PyCaret requires more than 100 lines of code in most libraries. The library also allows you to do more advanced things, such as advanced pre-processing, ensembling, generalized stacking, and other techniques that allow you to fully customize the ML pipeline and are a must for any data scientist. PyCaret is an open source, low-level library for ML with Python that allows you to go from preparing your data to deploying your model in minutes. Allows scientists and data analysts to perform iterative data science experiments from start to finish efficiently and allows them to reach conclusions faster because much less time is spent on programming. When working on a data science project, it usually takes a long time to understand the data (EDA and feature engineering). So, what if we could cut the time we spend on the modeling part of the project in half?

Just as the name implies, data science is a branch of science that applies the scientific method to data with the goal of studying the relationships between different features and drawing out meaningful conclusions based on these relationships. Data is, therefore, the key component in data science. A dataset is a particular instance of data that is used for analysis or model building at any given time. A dataset comes in different flavors such as numerical data, categorical data, text data, image data, voice data, and video data. A dataset could be static (not changing) or dynamic (changes with time, for example, stock prices).

Decision making under uncertainty is critical to real-world, autonomous systems. Model Predictive Control (MPC) methods have demonstrated favorable performance in practice, but remain limited when dealing with complex probability distributions. In this paper, we propose a generalization of MPC that represents a multitude of solutions as posterior distributions. By casting MPC as a Bayesian inference problem, we employ variational methods for posterior computation, naturally encoding the complexity and multi-modality of the decision making problem. We propose a Stein variational gradient descent method to estimate the posterior directly over control parameters, given a cost function and observed state trajectories. We show that this framework leads to successful planning in challenging, non-convex optimal control problems.

Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many others. Despite the existence of algorithms that learn the dynamics from trajectorial measurements there are few attempts to infer the dynamical system straight from population data. In this work, we deduce and then computationally estimate the Fokker-Planck equation which describes the evolution of the population's probability density, based on stochastic differential equations. Then, following the USDL approach, we project the Fokker-Planck equation to a proper set of test functions, transforming it into a linear system of equations. Finally, we apply sparse inference methods to solve the latter system and thus induce the driving forces of the dynamical system. Our approach is illustrated in both synthetic and real data including non-linear, multimodal stochastic differential equations, biochemical reaction networks as well as mass cytometry biological measurements.

KNN classification is a query triggered yet improvisational learning mode, in which they are carried out only when a test data is predicted that set a suitable K value and search the K nearest neighbors from the whole training sample space, referred them to the lazy part of KNN classification. This lazy part has been the bottleneck problem of applying KNN classification. In this paper, a one-step computation is proposed to replace the lazy part of KNN classification. The one-step computation actually transforms the lazy part to a matrix computation as follows. Given a test data, training samples are first applied to fit the test data with the least squares loss function. And then, a relationship matrix is generated by weighting all training samples according to their influence on the test data. Finally, a group lasso is employed to perform sparse learning of the relationship matrix. In this way, setting K value and searching K nearest neighbors are both integrated to a unified computation. In addition, a new classification rule is proposed for improving the performance of one-step KNN classification. The proposed approach is experimentally evaluated, and demonstrated that the one-step KNN classification is efficient and promising.

Prediction and quantification of future volatility and returns play an important role in financial modelling, both in portfolio optimization and risk management. Natural language processing today allows to process news and social media comments to detect signals of investors' confidence. We have explored the relationship between sentiment extracted from financial news and tweets and FTSE100 movements. We investigated the strength of the correlation between sentiment measures on a given day and market volatility and returns observed the next day. The findings suggest that there is evidence of correlation between sentiment and stock market movements: the sentiment captured from news headlines could be used as a signal to predict market returns; the same does not apply for volatility. Also, in a surprising finding, for the sentiment found in Twitter comments we obtained a correlation coefficient of -0.7, and p-value below 0.05, which indicates a strong negative correlation between positive sentiment captured from the tweets on a given day and the volatility observed the next day. We developed an accurate classifier for the prediction of market volatility in response to the arrival of new information by deploying topic modelling, based on Latent Dirichlet Allocation, to extract feature vectors from a collection of tweets and financial news. The obtained features were used as additional input to the classifier. Thanks to the combination of sentiment and topic modelling our classifier achieved a directional prediction accuracy for volatility of 63%.

Causality understanding between events is a critical natural language processing task that is helpful in many areas, including health care, business risk management and finance. On close examination, one can find a huge amount of textual content both in the form of formal documents or in content arising from social media like twitter, dedicated to communicating and exploring various types of causality in the real world. Recognizing these "Cause-Effect" relationships between natural language events continues to remain a challenge simply because it is often expressed implicitly. Implicit causality is hard to detect through most of the techniques employed in literature and can also, at times be perceived as ambiguous or vague. Also, although well known datasets do exist for this problem, the examples in them are limited in the range and complexity of the causal relationships they depict especially when related to implicit relationships. Most of the contemporary methods are either based on lexico-semantic pattern matching or are feature-driven supervised methods. Therefore, as expected these methods are more geared towards handling explicit causal relationships leading to limited coverage for implicit relationships and are hard to generalize. In this paper, we investigate the language model's capabilities for causal association among events expressed in natural language text using sentence context combined with event information, and by leveraging masked event context with in-domain and out-of-domain data distribution. Our proposed methods achieve the state-of-art performance in three different data distributions and can be leveraged for extraction of a causal diagram and/or building a chain of events from unstructured text.

Bipartite graph embedding has recently attracted much attention due to the fact that bipartite graphs are widely used in various application domains. Most previous methods, which adopt random walk-based or reconstruction-based objectives, are typically effective to learn local graph structures. However, the global properties of bipartite graph, including community structures of homogeneous nodes and long-range dependencies of heterogeneous nodes, are not well preserved. In this paper, we propose a bipartite graph embedding called BiGI to capture such global properties by introducing a novel local-global infomax objective. Specifically, BiGI first generates a global representation which is composed of two prototype representations. BiGI then encodes sampled edges as local representations via the proposed subgraph-level attention mechanism. Through maximizing the mutual information between local and global representations, BiGI enables nodes in bipartite graph to be globally relevant. Our model is evaluated on various benchmark datasets for the tasks of top-K recommendation and link prediction. Extensive experiments demonstrate that BiGI achieves consistent and significant improvements over state-of-the-art baselines. Detailed analyses verify the high effectiveness of modeling the global properties of bipartite graph.