The simplest solutions are usually the most powerful ones, and Naïve Bayes is a good example of that. Despite the advances in Machine Learning in the last years, it has proven to not only be simple but also fast, accurate, and reliable. It has been successfully used for many purposes, but it works particularly well with natural language processing (NLP) problems. Naïve Bayes is a probabilistic machine learning algorithm based on the Bayes Theorem, used in a wide variety of classification tasks. In this article, we will understand the Naïve Bayes algorithm and all essential concepts so that there is no room for doubts in understanding.

Gaussian ODE filtering is a probabilistic numerical method to solve ordinary differential equations (ODEs). It computes a Bayesian posterior over the solution from evaluations of the vector field defining the ODE. Its most popular version, which employs an integrated Brownian motion prior, uses Taylor expansions of the mean to extrapolate forward and has the same convergence rates as classical numerical methods. As the solution of many important ODEs are periodic functions (oscillators), we raise the question whether Fourier expansions can also be brought to bear within the framework of Gaussian ODE filtering. To this end, we construct a Fourier state space model for ODEs and a `hybrid' model that combines a Taylor (Brownian motion) and Fourier state space model. We show by experiments how the hybrid model might become useful in cheaply predicting until the end of the time domain.

We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large and complex spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hasting ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel architecture through the integration of a parallel EA framework that guides Markov chains running in parallel.

We study the problem of policy optimization in Markov Decision Process over infinite time horizons (Puterman, 1994). We focus on the batch (i.e., off-line) setting, where historical data of multiple trajectories has been previously collected using some behavior policy. Our goal is to learn a new policy with guaranteed performance when implemented in the future. In this work, we develop a data-efficient method to learn the policy that optimizes the long-term average reward in a pre-specified policy class from a training set composed of multiple trajectories. Furthermore, we establish a finite-sample regret guarantee, i.e., the difference between the average reward of the optimal policy in the class and the average reward of the estimated policy by our proposed method. This work is motivated by the development of justin-time adaptive intervention in mobile health (mHealth) applications (Nahum-Shani et al., 2017). Our method can be used to learn a treatment policy that maps the real-time collected information about the individual's status and context to a particular treatment at each of many decision times to support health behaviors.

Multi-reference alignment entails estimating a signal in $\mathbb{R}^L$ from its circularly-shifted and noisy copies. This problem has been studied thoroughly in recent years, focusing on the finite-dimensional setting (fixed $L$). Motivated by single-particle cryo-electron microscopy, we analyze the sample complexity of the problem in the high-dimensional regime $L\to\infty$. Our analysis uncovers a phase transition phenomenon governed by the parameter $\alpha = L/(\sigma^2\log L)$, where $\sigma^2$ is the variance of the noise. When $\alpha>2$, the impact of the unknown circular shifts on the sample complexity is minor. Namely, the number of measurements required to achieve a desired accuracy $\varepsilon$ approaches $\sigma^2/\varepsilon$ for small $\varepsilon$; this is the sample complexity of estimating a signal in additive white Gaussian noise, which does not involve shifts. In sharp contrast, when $\alpha\leq 2$, the problem is significantly harder and the sample complexity grows substantially quicker with $\sigma^2$.

In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide identifiability results for SSMF rely on the sufficiently scattered condition (SSC) which requires the data points to be well spread within the convex hull of the basis vectors. The conditions under which our proposed algorithms recover the unique decomposition is in most cases much weaker than the SSC. We only require to have $d$ points on each facet of the convex hull of the basis vectors whose dimension is $d-1$. The key idea is based on extracting facets containing the largest number of points. We illustrate the effectiveness of our approach on synthetic data sets and hyperspectral images, showing that it outperforms state-of-the-art SSMF algorithms as it is able to handle higher noise levels, rank deficient matrices, outliers, and input data that highly violates the SSC.

The scope of a lucrative career promoted by Google through its video distribution platform YouTube has attracted a large number of users to become content creators. An important aspect of this line of work is the feedback received in the form of comments which show how well the content is being received by the audience. However, volume of comments coupled with spam and limited tools for comment classification makes it virtually impossible for a creator to go through each and every comment and gather constructive feedback. Automatic classification of comments is a challenge even for established classification models, since comments are often of variable lengths riddled with slang, symbols and abbreviations. This is a greater challenge where comments are multilingual as the messages are often rife with the respective vernacular. In this work, we have evaluated top-performing classification models for classifying comments which are a mix of different combinations of English and Malayalam (only English, only Malayalam and Mix of English and Malayalam). The statistical analysis of results indicates that Multinomial Naive Bayes, K-Nearest Neighbors (KNN), Support Vector Machine (SVM), Random Forest and Decision Trees offer similar level of accuracy in comment classification. Further, we have also evaluated 3 multilingual transformer based language models (BERT, DISTILBERT and XLM) and compared their performance to the traditional machine learning classification techniques. XLM was the top-performing BERT model with an accuracy of 67.31. Random Forest with Term Frequency Vectorizer was the best performing model out of all the traditional classification models with an accuracy of 63.59.

The ability to learn effective transformations of complex data sources, sometimes called representation learning, is an essential primitive in modern machine learning, leading to remarkable achievements in language modeling, vision, and serving as a partial explanation for the success of deep learning more broadly (Bengio et al., 2013). In Reinforcement Learning (RL), several works have shown empirically that learning succinct representations of perceptual inputs can accelerate the search for decision-making policies (Pathak et al., 2017; Tang et al., 2017; Oord et al., 2018; Srinivas et al., 2020). However, representation learning for RL is far more subtle than it is for supervised learning (Du et al., 2019a; Van Roy and Dong, 2019; Lattimore and Szepesvari, 2019), and the theoretical foundations of representation learning for RL are nascent. The first question that arises in this context is: what is a good representation? Intuitively, a good representation should help us achieve greater sample efficiency on downstream tasks.

There are multiple ways to estimate a Stan model in R, but I choose to build the Stan code directly rather than using the brms or rstanarm packages. In the Stan code, we need to define the data structure, specify the parameters, specify any transformed parameters (which are just a function of the parameters), and then build the model – which includes laying out the prior distributions as well as the likelihood. In this case, the model is slightly different from what was presented in the context of a mixed effects model. The key difference is that there are prior distributions on \(\Delta\) and \(\tau\), introducing an additional level of uncertainty into the estimate. I would expect that the estimate of the overall treatment effect \(\Delta\) will have a wider 95% CI (credible interval in this context) than the 95% CI (confidence interval) for \(\delta_0\) in the mixed effects model.

Designing efficient algorithms that learn and plan in sequential decision-making tasks with large state and action spaces has become the central goal of modern reinforcement learning (RL) in recent years. Due to numerous possible states and actions, traditional tabular reinforcement learning methods (Watkins, 1989; Jaksch et al., 2010; Azar et al., 2017) which directly access each stateaction pair are computationally intractable. A common method to design reinforcement learning algorithms for large-scale state and action spaces is to make use of feature mappings such as linear functions or neural networks to map states and actions to a low-dimensional space and solve the decision-making problem in the feature space. Despite the empirical success of feature mapping based reinforcement learning methods (Singh et al., 1995; Kwok and Fox, 2004; Bertsekas, 2018), the theoretical understanding and the fundamental limits of these methods remain largely understudied. In this paper, we aim to develop provable reinforcement learning algorithms with feature mapping for discounted Markov Decision Processes (MDPs). Discounted MDP is one of the most widely used models to formulate the modern reinforcement learning tasks such as Atari games (Mnih et al., 2015) and deep recommendation system (Zheng et al., 2018).