The overwhelming presence of categorical/sequential data in diverse domains emphasizes the importance of sequence mining. The challenging nature of sequences proves the need for continuing research to find a more accurate and faster approach providing a better understanding of their (dis)similarities. This paper proposes a new Model-based approach for clustering sequence data, namely nTreeClus. The proposed method deploys Tree-based Learners, k-mers, and autoregressive models for categorical time series, culminating with a novel numerical representation of the categorical sequences. Adopting this new representation, we cluster sequences, considering the inherent patterns in categorical time series. Accordingly, the model showed robustness to its parameter. Under different simulated scenarios, nTreeClus improved the baseline methods for various internal and external cluster validation metrics for up to 10.7% and 2.7%, respectively. The empirical evaluation using synthetic and real datasets, protein sequences, and categorical time series showed that nTreeClus is competitive or superior to most state-of-the-art algorithms.

Embedding methods for mixed-curvature spaces are powerful techniques for low-distortion and low-dimensional representation of complex data structures. Nevertheless, little is known regarding downstream learning and optimization in the embedding space. Here, we address for the first time the problem of linear classification in a product space form -- a mix of Euclidean, spherical, and hyperbolic spaces with different dimensions. First, we revisit the definition of a linear classifier on a Riemannian manifold by using geodesics and Riemannian metrics which generalize the notions of straight lines and inner products in vector spaces, respectively. Second, we prove that linear classifiers in $d$-dimensional constant curvature spaces can shatter exactly $d+1$ points: Hence, Euclidean, hyperbolic and spherical classifiers have the same expressive power. Third, we formalize linear classifiers in product space forms, describe a novel perceptron classification algorithm, and establish rigorous convergence results. We support our theoretical findings with simulation results on several datasets, including synthetic data, MNIST and Omniglot. Our results reveal that learning methods applied to small-dimensional embeddings in product space forms significantly outperform their algorithmic counterparts in Euclidean spaces.

Motivated by biological considerations, we study sparse neural maps from an input layer to a target layer with sparse activity, and specifically the problem of storing $K$ input-target associations $(x,y)$, or memories, when the target vectors $y$ are sparse. We mathematically prove that $K$ undergoes a phase transition and that in general, and somewhat paradoxically, sparsity in the target layers increases the storage capacity of the map. The target vectors can be chosen arbitrarily, including in random fashion, and the memories can be both encoded and decoded by networks trained using local learning rules, including the simple Hebb rule. These results are robust under a variety of statistical assumptions on the data. The proofs rely on elegant properties of random polytopes and sub-gaussian random vector variables. Open problems and connections to capacity theories and polynomial threshold maps are discussed.

We propose a distributed bootstrap method for simultaneous inference on high-dimensional massive data that are stored and processed with many machines. The method produces a $\ell_\infty$-norm confidence region based on a communication-efficient de-biased lasso, and we propose an efficient cross-validation approach to tune the method at every iteration. We theoretically prove a lower bound on the number of communication rounds $\tau_{\min}$ that warrants the statistical accuracy and efficiency. Furthermore, $\tau_{\min}$ only increases logarithmically with the number of workers and intrinsic dimensionality, while nearly invariant to the nominal dimensionality. We test our theory by extensive simulation studies, and a variable screening task on a semi-synthetic dataset based on the US Airline On-time Performance dataset. The code to reproduce the numerical results is available at GitHub: https://github.com/skchao74/Distributed-bootstrap.

Deep convolutional models have been at the heart of the recent successes of deep learning in problems where the data consists of high-dimensional signals, such as image classification or speech recognition. The convolution and pooling operations in these architectures are known to be crucial for their practical success, yet our theoretical understanding of how they enable efficient learning is still limited. One key difficulty for understanding such models is the curse of dimensionality: due to the highdimensionality of the input data, it is hopeless to learn arbitrary functions from samples. For instance, classical non-parametric regression techniques for approximating Lipschitz or Sobolev functions typically require either low dimension or an order of smoothness of the target function comparable to the dimension in order to obtain good generalization (e.g., Wainwright, 2019), which is a very strong assumption when dealing with high-dimensional signals. Thus, further assumptions on the target function are needed to make the problem more tractable, in a way that makes convolutions a useful modeling tool. Various works have studied approximation benefits with models that resemble deep convolutional architectures, for instance through hierarchical models with local connectivity (Mhaskar and Poggio, 2016; Schmidt-Hieber et al., 2020), or through structured tensor decompositions (Cohen and Shashua, 2017). Nevertheless, while such function classes may provide improved statistical efficiency, it is unclear if they can be learned with computationally efficient algorithms, which makes it difficult to assess the validity of these approximation models empirically. In order to overcome the computational difficulties, we provide a different perspective based on kernel methods (e.g., Schölkopf and Smola, 2001; Wahba, 1990), which are known to be computationally tractable with well-understood statistical and approximation properties. In particular, we consider "deep" structured kernels known as convolutional kernels, which have produced good empirical performance on standard

In offline reinforcement learning (RL) an optimal policy is learnt solely from a priori collected observational data. However, in observational data, actions are often confounded by unobserved variables. Instrumental variables (IVs), in the context of RL, are the variables whose influence on the state variables are all mediated through the action. When a valid instrument is present, we can recover the confounded transition dynamics through observational data. We study a confounded Markov decision process where the transition dynamics admit an additive nonlinear functional form. Using IVs, we derive a conditional moment restriction (CMR) through which we can identify transition dynamics based on observational data. We propose a provably efficient IV-aided Value Iteration (IVVI) algorithm based on a primal-dual reformulation of CMR. To the best of our knowledge, this is the first provably efficient algorithm for instrument-aided offline RL.

This paper studies fixed step-size stochastic approximation (SA) schemes, including stochastic gradient schemes, in a Riemannian framework. It is motivated by several applications, where geodesics can be computed explicitly, and their use accelerates crude Euclidean methods. A fixed step-size scheme defines a family of time-homogeneous Markov chains, parametrized by the step-size. Here, using this formulation, non-asymptotic performance bounds are derived, under Lyapunov conditions. Then, for any step-size, the corresponding Markov chain is proved to admit a unique stationary distribution, and to be geometrically ergodic. This result gives rise to a family of stationary distributions indexed by the step-size, which is further shown to converge to a Dirac measure, concentrated at the solution of the problem at hand, as the step-size goes to 0. Finally, the asymptotic rate of this convergence is established, through an asymptotic expansion of the bias, and a central limit theorem.

Sentiment analysis is a vast area in the Machine learning domain. A lot of work is done on datasets and their analysis of the English Language. In Pakistan, a huge amount of data is in roman Urdu language, it is scattered all over the social sites including Twitter, YouTube, Facebook and similar applications. In this study the focus domain of dataset gathering is YouTube comments. The Dataset contains the comments of people over different Pakistani dramas and TV shows. The Dataset contains multi-class classification that is grouped The comments into positive, negative and neutral sentiment. In this Study comparative analysis is done for five supervised learning Algorithms including linear regression, SVM, KNN, Multi layer Perceptron and Na\"ive Bayes classifier. Accuracy, recall, precision and F-measure are used for measuring performance. Results show that accuracy of SVM is 64 percent, which is better than the rest of the list.

The Kalman filter is a fundamental filtering algorithm that fuses noisy sensory data, a previous state estimate, and a dynamics model to produce a principled estimate of the current state. It assumes, and is optimal for, linear models and white Gaussian noise. Due to its relative simplicity and general effectiveness, the Kalman filter is widely used in engineering applications. Since many sensory problems the brain faces are, at their core, filtering problems, it is possible that the brain possesses neural circuitry that implements equivalent computations to the Kalman filter. The standard approach to Kalman filtering requires complex matrix computations that are unlikely to be directly implementable in neural circuits. In this paper, we show that a gradient-descent approximation to the Kalman filter requires only local computations with variance weighted prediction errors. Moreover, we show that it is possible under the same scheme to adaptively learn the dynamics model with a learning rule that corresponds directly to Hebbian plasticity. We demonstrate the performance of our method on a simple Kalman filtering task, and propose a neural implementation of the required equations. The Bayesian Brain hypothesis has gained significant traction in cognitive neuroscience over the last two decades (Knill and Pouget, 2004; Doya et al., 2007; Pouget et al., 2013).

The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in real-world VRP applications, Machine Learning (ML) methods have been used in combination with analytical approaches to enhance problem formulations and algorithmic performance across different problem solving scenarios. However, the relevant papers are scattered in several traditional research fields with very different, sometimes confusing, terminologies. This paper presents a first, comprehensive review of hybrid methods that combine analytical techniques with ML tools in addressing VRP problems. Specifically, we review the emerging research streams on ML-assisted VRP modelling and ML-assisted VRP optimisation. We conclude that ML can be beneficial in enhancing VRP modelling, and improving the performance of algorithms for both online and offline VRP optimisations. Finally, challenges and future opportunities of VRP research are discussed.