A regression model is a statistical model that estimates the relationship between one dependent variable and one or more independent variables using a line (or a plane in the case of two or more independent variables). Multiple linear regression (MLR), also known simply as multiple regression, is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. Multiple regression is an extension of linear (OLS) regression that uses just one explanatory variable. Let's try to predict of startups using Multiple Linear Regression in Python We will be using Scikit-learn Library to import the necessary functions required for this Exercise. We will be using Pandas and Numpy for Data Exploration.

This article was published as a part of the Data Science Blogathon. Mobile phones come in all sorts of prices, features, specifications and all. Price estimation and prediction is an important part of consumer strategy. Deciding on the correct price of a product is very important for the market success of a product. A new product that has to be launched, must have the correct price so that consumers find it appropriate to buy the product.

In recent years, the methods on matrix-based or bilinear discriminant analysis (BLDA) have received much attention. Despite their advantages, it has been reported that the traditional vector-based regularized LDA (RLDA) is still quite competitive and could outperform BLDA on some benchmark datasets. Nevertheless, it is also noted that this finding is mainly limited to image data. In this paper, we propose regularized BLDA (RBLDA) and further explore the comparison between RLDA and RBLDA on another type of matrix data, namely multivariate time series (MTS). Unlike image data, MTS typically consists of multiple variables measured at different time points. Although many methods for MTS data classification exist within the literature, there is relatively little work in exploring the matrix data structure of MTS data. Moreover, the existing BLDA can not be performed when one of its within-class matrices is singular. To address the two problems, we propose RBLDA for MTS data classification, where each of the two within-class matrices is regularized via one parameter. We develop an efficient implementation of RBLDA and an efficient model selection algorithm with which the cross validation procedure for RBLDA can be performed efficiently. Experiments on a number of real MTS data sets are conducted to evaluate the proposed algorithm and compare RBLDA with several closely related methods, including RLDA and BLDA. The results reveal that RBLDA achieves the best overall recognition performance and the proposed model selection algorithm is efficient; Moreover, RBLDA can produce better visualization of MTS data than RLDA.

This paper is an extended version of [Burashnikova et al., 2021, arXiv: 2012.06910], where we proposed a theoretically supported sequential strategy for training a large-scale Recommender System (RS) over implicit feedback, mainly in the form of clicks. The proposed approach consists in minimizing pairwise ranking loss over blocks of consecutive items constituted by a sequence of non-clicked items followed by a clicked one for each user. We present two variants of this strategy where model parameters are updated using either the momentum method or a gradient-based approach. To prevent updating the parameters for an abnormally high number of clicks over some targeted items (mainly due to bots), we introduce an upper and a lower threshold on the number of updates for each user. These thresholds are estimated over the distribution of the number of blocks in the training set. They affect the decision of RS by shifting the distribution of items that are shown to the users. Furthermore, we provide a convergence analysis of both algorithms and demonstrate their practical efficiency over six large-scale collections with respect to various ranking measures.

In machine learning, crowdsourcing is an economical way to label a large amount of data. However, the noise in the produced labels may deteriorate the accuracy of any classification method applied to the labelled data. We propose an enhanced nearest neighbor classifier (ENN) to overcome this issue. Two algorithms are developed to estimate the worker quality (which is often unknown in practice): one is to construct the estimate based on the denoised worker labels by applying the $k$NN classifier to the expert data; the other is an iterative algorithm that works even without access to the expert data. Other than strong numerical evidence, our proposed methods are proven to achieve the same regret as its oracle version based on high-quality expert data. As a technical by-product, a lower bound on the sample size assigned to each worker to reach the optimal convergence rate of regret is derived.

Frequentist and Bayesian are two different versions of statistics. Frequentist is a more classical version, which, as the name suggests, rely on the long run frequency of events (data points) to calculate the variable of interest. Bayesian on the other hand, can also work without having a large number of events (in fact, it could work even with one data point!). The cardinal difference between the two is that: frequentist will give you a point estimate, whereas Bayesian will give you a distribution. Having a point estimate means that -- "we are certain that this is the output for this variable of interest". Whereas, having a distribution can be interpreted as -- "we have some belief that the mean of the distribution is the good estimate for this variable of interest, but there is uncertainty too, in the form of standard deviation".

Welcome to Time Series Analysis, Forecasting, and Machine Learning in Python. Time Series Analysis has become an especially important field in recent years. With inflation on the rise, many are turning to the stock market and cryptocurrencies in order to ensure their savings do not lose their value. COVID-19 has shown us how forecasting is an essential tool for driving public health decisions. Businesses are becoming increasingly efficient, forecasting inventory and operational needs ahead of time.

Raman spectroscopy is an effective, low-cost, non-intrusive technique often used for chemical identification. Typical approaches are based on matching observations to a reference database, which requires careful preprocessing, or supervised machine learning, which requires a fairly large number of training observations from each class. We propose a new machine learning technique for Raman spectrum matching, based on contrastive representation learning, that requires no preprocessing and works with as little as a single reference spectrum from each class. On three datasets we demonstrate that our approach significantly improves or is on par with the state of the art in prediction accuracy, and we show how to compute conformal prediction sets with specified frequentist coverage. Based on our findings, we believe contrastive representation learning is a promising alternative to existing methods for Raman spectrum matching.

We introduce the first direct policy search algorithm which provably converges to the globally optimal $\textit{dynamic}$ filter for the classical problem of predicting the outputs of a linear dynamical system, given noisy, partial observations. Despite the ubiquity of partial observability in practice, theoretical guarantees for direct policy search algorithms, one of the backbones of modern reinforcement learning, have proven difficult to achieve. This is primarily due to the degeneracies which arise when optimizing over filters that maintain internal state. In this paper, we provide a new perspective on this challenging problem based on the notion of $\textit{informativity}$, which intuitively requires that all components of a filter's internal state are representative of the true state of the underlying dynamical system. We show that informativity overcomes the aforementioned degeneracy. Specifically, we propose a $\textit{regularizer}$ which explicitly enforces informativity, and establish that gradient descent on this regularized objective - combined with a ``reconditioning step'' - converges to the globally optimal cost a $\mathcal{O}(1/T)$ rate. Our analysis relies on several new results which may be of independent interest, including a new framework for analyzing non-convex gradient descent via convex reformulation, and novel bounds on the solution to linear Lyapunov equations in terms of (our quantitative measure of) informativity.

Estimating heterogeneous treatment effects is an important problem across many domains. In order to accurately estimate such treatment effects, one typically relies on data from observational studies or randomized experiments. Currently, most existing works rely exclusively on observational data, which is often confounded and, hence, yields biased estimates. While observational data is confounded, randomized data is unconfounded, but its sample size is usually too small to learn heterogeneous treatment effects. In this paper, we propose to estimate heterogeneous treatment effects by combining large amounts of observational data and small amounts of randomized data via representation learning. In particular, we introduce a two-step framework: first, we use observational data to learn a shared structure (in form of a representation); and then, we use randomized data to learn the data-specific structures. We analyze the finite sample properties of our framework and compare them to several natural baselines. As such, we derive conditions for when combining observational and randomized data is beneficial, and for when it is not. Based on this, we introduce a sample-efficient algorithm, called CorNet. We use extensive simulation studies to verify the theoretical properties of CorNet and multiple real-world datasets to demonstrate our method's superiority compared to existing methods.