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What are the top 3 methods used to find Autoregressive Parameters in Data Science?
In order to find autoregressive parameters, you will first need to understand what autoregression is. Autoregression is a statistical method used to create a model that describes data as a function of linear regression of lagged values of the dependent variable. In other words, it is a model that uses past values of a dependent variable in order to predict future values of the same dependent variable.
In time series analysis, autoregression is the use of previous values in a time series to predict future values. In other words, it is a form of regression where the dependent variable is forecasted using a linear combination of past values of the independent variable. The parameter values for the autoregression model are estimated using the method of least squares.
The autoregressive parameters are the coefficients in the autoregressive model. These coefficients can be estimated in a number of ways, including ordinary least squares (OLS), maximum likelihood (ML), or least squares with L1 regularization (LASSO). Once estimated, the autoregressive parameters can be used to predict future values of the dependent variable.
To find the autoregressive parameters, you need to use a method known as least squares regression. This method finds the parameters that minimize the sum of the squared residuals. The residual is simply the difference between the predicted value and the actual value. So, in essence, you are finding the parameters that best fit the data.
How to Estimate Autoregressive Parameters?
There are three main ways to estimate autoregressive parameters: ordinary least squares (OLS), maximum likelihood (ML), or least squares with L1 regularization (LASSO).
Ordinary Least Squares: Ordinary least squares is the simplest and most common method for estimating autoregressive parameters. This method estimates the parameters by minimizing the sum of squared errors between actual and predicted values.
Maximum Likelihood: Maximum likelihood is another common method for estimating autoregressive parameters. This method estimates the parameters by maximizing the likelihood function. The likelihood function is a mathematical function that quantifies the probability of observing a given set of data given certain parameter values.
Least Squares with L1 Regularization: Least squares with L1 regularization is another method for estimating autoregressive parameters. This method estimates the parameters by minimizing the sum of squared errors between actual and predicted values while also penalizing models with many parameters. L1 regularization penalizes models by adding an extra term to the error function that is proportional to the sum of absolute values of the estimator coefficients.
Finding Autoregressive Parameters: The Math Behind It To find the autoregressive parameters using least squares regression, you first need to set up your data in a certain way. You need to have your dependent variable in one column and your independent variables in other columns. For example, let’s say you want to use three years of data to predict next year’s sales (the dependent variable). Your data would look something like this:
$$ \hat {\beta }=(X^{\prime }X)^{-1}X^{\prime }Y=\frac {1}{2500}\times 2500\times (-500)=0.20 $$\.20 . That’s it! Our autoregressive parameter is 0\.20 . Once we have that parameter, we can plug it into our autoregressive equation:
$$ Y_{t+1}=0\.20 Y_t+a_1+a_2+a_3footnote{where $a_1$, $a_2$, and $a_3$ are error terms assuming an AR(3)} .$$ And that’s how you solve for autoregressive parameters! Of course, in reality you would be working with much larger datasets, but the underlying principles are still the same. Once you have your autoregressive parameters, you can plug them into the equation and start making predictions!.
Which Method Should You Use? The estimation method you should use depends on your particular situation and goals. If you are looking for simple and interpretable results, then Ordinary Least Squares may be the best method for you. If you are looking for more accurate predictions, then Maximum Likelihood or Least Squares with L1 Regularization may be better methods for you.
Autoregressive models STEP BY STEP:
1) Download data: The first step is to download some data. This can be done by finding a publicly available dataset or by using your own data if you have any. For this example, we will be using data from the United Nations Comtrade Database.
2) Choose your variables: Once you have your dataset, you will need to choose the variables you want to use in your autoregression model. In our case, we will be using the import and export values of goods between countries as our independent variables.
3) Estimate your model: After choosing your independent variables, you can estimate your autoregression model using the method of least squares. OLS estimation can be done in many statistical software packages such as R or STATA.
4) Interpret your results: Once you have estimated your model, it is important to interpret the results in order to understand what they mean. The coefficients represent the effect that each independent variable has on the dependent variable. In our case, the coefficients represent the effect that imports and exports have on trade balance. A positive coefficient indicates that an increase in the independent variable leads to an increase in the dependent variable while a negative coefficient indicates that an increase in the independent variable leads to a decrease in the dependent variable.
5)Make predictions: Finally, once you have interpreted your results, you can use your autoregression model to make predictions about future values of the dependent variable based on past values of the independent variables.
Conclusion: In this blog post, we have discussed what autoregression is and how to find autoregressive parameters.
Estimating an autoregression model is a relatively simple process that can be done in many statistical software packages such as R or STATA.
In statistics and machine learning, autoregression is a modeling technique used to describe the linear relationship between a dependent variable and one more independent variables. To find the autoregressive parameters, you can use a method known as least squares regression which minimizes the sum of squared residuals. This blog post also explains how to set up your data for calculating least squares regression as well as how to calculate Variance and Covariance before finally calculating your autoregressive parameters. After finding your parameters you can plug them into an autoregressive equation to start making predictions about future events!
We have also discussed three different methods for estimating those parameters: Ordinary Least Squares, Maximum Likelihood, and Least Squares with L1 Regularization. The appropriate estimation method depends on your particular goals and situation.
Autoregressive generative models can estimate complex continuous data distributions such as trajectory rollouts in an RL environment, image intensities, and audio. Traditional techniques discretize continuous data into various bins and approximate the continuous data distribution using categorical distributions over the bins. This approximation is parameter inefficient as it cannot express abrupt changes in density without using a significant number of additional bins. Adaptive Categorical Discretization (ADACAT) is proposed in this paper as a parameterization of 1-D conditionals that is expressive, parameter efficient, and multimodal. A vector of interval widths and masses is used to parameterize the distribution known as ADACAT. Figure 1 showcases the difference between the traditional uniform categorical discretization approach with the proposed ADACAT.
Each component of the ADACAT distribution has non-overlapping support, making it a specific subfamily of mixtures of uniform distributions. ADACAT generalizes uniformly discretized 1-D categorical distributions. The proposed architecture allows for variable bin widths and more closely approximates the modes of two Gaussians mixture than a uniformly discretized categorical, making it highly expressive than the latter. Additionally, a distribution’s support is discretized using quantile-based discretization, which bins data into groups with similar measured data points. ADACAT uses deep autoregressive frameworks to factorize the joint density into numerous 1-D conditional ADACAT distributions in problems with more than one dimension.
I am on a good level now and I want to practice what I have learned, but most of the projects online are far from practical and I want to do something close to reality so If anyone here works as a DA or BI , can you please direct me to projects online that you find close to what you work with ? submitted by /u/Emotional-Rhubarb725 [link] [comments]
I worked as a civil engineer for 5 years before getting a Hydroinformatics position (primarily data analysis with some elements of machine learning applied to wastewater) and and am looking to move into an official data science position. I haven’t gotten any hits while applying to various roles but I’ve been leaving out my engineering experience since I don’t want to work in anything related to engineering. Wondering if this is a bad idea and if I should just put the experience back on my resume? submitted by /u/GoldenPandaCircus [link] [comments]
Hi all, As the title implies, I've been relying on (somewhat near) real-time monitoring of model performance metrics to see if data drift has happened in my use-case. I'm wondering if you know other more sophisticated/advanced methods to detect data drift. Would love to hear any kind of methods, whether they target detection of covariate/feature drift, target/label drift or concept drift. Even better if you can share any Python or R implementations to carry out the above data drift checks. Thanks in advance! submitted by /u/YsrYsl [link] [comments]
Hi, I’m at the beginning of my career. Currently, my main focus has been to get into data science (product side), then maybe in the future decide to become a PM or stay in DS, depending on the role and company I get. Recently, I came across a company hiring for a Sales Engineer position. The company is a SaaS for data science, so I researched the role and felt I would like it. I do enjoy working with people, presenting things, and public speaking if required. I’ve heard the pay is pretty good in sales engineering too. However, I was wondering if I didn’t like it after a few months or years, would it be possible to come back to product or data science? I do like the data science field as I’m curious about finding insights, solving problems, and on the product side, improving user experiences and creating new features. I’ve been looking for an opportunity since last year and haven’t been able to land a job, not even as an analyst. So my fear is if I get into sales engineering (I’m only interested in this particular firm for this role), would it be hard to get back into the industry? I’m currently working as a volunteer data science to maintain visa, so not like I will be leaving actual DS job. Also, I don’t know if I will get the role for SE as well, but wanted to decide as I have someone who will refer me and i feared that it would look bad when I ask them for referral for data science role (in future as they don’t have any open role now for DS). Also, in the long term, I was thinking if money is the biggest driver for me, which would be better? Additionally, I’m an international on a STEM visa in the US. So, how hard is it for other firms to sponsor a sales engineering role? Thanks! submitted by /u/Starktony11 [link] [comments]
I have the opportunity to take two jobs. One is for a senior BI analyst at a medium-sized sports betting company ($500M revenue) and the other is for a “reporting analyst” position with a large asset management firm (>$1B revenue). Here is my dilemma: - The BI analyst one involves a lot more data science methodology and probably offers more direct advancement in this field The reporting analyst one is mostly focused on outreach and data collection (calling member banks and whatnot) to report investment data to supervisors however, I would prefer to work in the financial industry long term as I enjoy economic data more and enjoy the idea of working within capital Markets and economic planning. I’m worried that if I take the sports betting role, I wont be able to pivot into this field later on. I would appreciate any and all advice. submitted by /u/OutrageousPressure6 [link] [comments]
I'm a senior Data Scientist/Machine Learning Engineer with 7 years of experience and a Kaggle Grandmaster. I just finished the first round of interviews at Jane Street. I think I did okay—I managed to come up with a somewhat decent solution, although I got stuck a few times. I don’t really understand the rationale behind asking LeetCode-style questions for MLE positions. The interviewer was nice, but when I asked about the responsibilities of MLEs at Jane Street, he had no idea. I’m not sure how to feel about this process, but it doesn’t make much sense to me. submitted by /u/BurnerMcBurnersonne [link] [comments]
Forecasting is still very clumsy and very painful. Even the models built by major companies -- Meta's Prophet and Google's Causal Impact come to mind -- don't really succeed as one-step, plug-and-play forecasting tools. They miss a lot of seasonality, overreact to outliers, and need a lot of tweaking to get right. It's an area of data science where the models that I build on my own tend to work better than the models I can find. LLMs, on the other hand, have reached incredible versatility and usability. ChatGPT and its clones aren't necessarily perfect yet, but they're definitely way beyond what I can do. Any time I have a language processing challenge, I know I'm going to get a better result leveraging somebody else's model than I will trying to build my own solution. Why is that? After all the time we as data scientists have put into forecasting, why haven't we created something that outperforms what an individual data scientist can create? Or -- if I'm wrong, and that does exist -- what tool does that? submitted by /u/takenorinvalid [link] [comments]
I was given the title of Director of Data after only 3 years of being a Data Analyst. I am a one-man department in a company of ~30 employees with ~$6-7 million in revenue/yr. I only recently hired a direct report part-time to assist with some of the more mundane tasks. I was given the title because I routinely deal with executives. The management at my company wants them to view me more as an equal rather than reaching out to them and they just forward to me anyways to complete the data request. While I enjoy the pay bump and increase in autonomy, my goal is to work as an individual contributor at a high level (DA or DS) as I do not want to deal with direct reports if possible. Especially not ones that have to be micromanaged. I've noticed since my title change ~2 years ago recruiters reach out to me asking me to hire candidates rather than approaching me as a candidate. This makes me think this job title may be too early as I am not even 30 yet and I am not ready to settle into a management role long-term. Has anyone else had a similar experience and how did you deal with it? I am in a situation where my employer would be willing to essentially give me whatever title I want if I left on good terms when a company calls for a reference. Edit: for any new comments, I do not claim to be a Data Scientist. My role is a mix of data analyst and data engineer as I do both Ad Hoc analysis and manage our SQL database. Because I'm already getting paid around 120k, I would likely need to move into a Senior Data Analyst or entry level Data Scientist role to maintain my salary. And I likely could only enter a DS role after I finish my Masters in Data Science as my Bachelors is in Finance and my Python skills are still in the early stages. submitted by /u/Inception952 [link] [comments]
Which of these graduate level classes would be more beneficial in me getting a DS job? Which do you use more? Thanks! submitted by /u/Careless-Tailor-2317 [link] [comments]
How much bayesian inference are data scientists generally doing in their day to day work? Are there roles in specific areas of data science where that knowledge is needed? Marketing comes to mind but I’m not sure where else. By knowledge of Bayesian inference I mean building hierarchical Bayesian models or more complex models in languages like Stan. submitted by /u/AdFew4357 [link] [comments]
I have been a data science manager for a little more than two years and absolutely hate it. I used to be in analytics and then technical product manager for ML solutions and took on this role to gain people management experience. Biggest mistake of my life. I have been trying to get back to being an individual contributor but feel rusty at the moment. My relationship with my stakeholders are great. They love me and consequently I am not able to move back to my old role as it will leave a void in the current role. My skip level boss is the same and wouldn't allow it. I have been interviewing outside but not clearing interview primarily because I do not have anything to talk about my individual performance that's groundbreaking. I also feel like I need to get back to basics and start from scratch. Any advice on how to proceed? P.S. I don't like the people management part as I do not feel in control of my day. I manage 9 ICs and there's always some fire to put out. I also think I got the responsibility of a big portfolio without enough experience in management. submitted by /u/TheEmotionalNerd [link] [comments]
A huge part of this job is working with stakeholders to take their grand ideas and make them a reality. Naturally, there's gonna be trial and error, dead ends, talking through different approaches, and that's all fine. That's not what I'm complaining about. The problem is that these stakeholders are higher up in the company and they're just strapped for time. They don't think about the things they ask me to do until I'm actually in a meeting with them, then it turns into a lot of "yeah let's do it this way, no actually that won't work, wait no it will disregard that just do it the first way".... I'm sitting here with a pen and paper or onenote open trying to catch everything and I just simply can't. I've tried to summarize at the end of meetings what the next steps are that we've settled on, and it's intended to be a yes/no question but it just ends up turning into another stream of consciousness info dump that leaves me with more questions than answers. Often times I run into simple questions as I'm working through a project. They're yes/no or not much more involved than that, but whenever I try to email or chat with a stakeholder they ALWAYS want to just meet and then what should've been a 30 second call ends up going past the hour mark, and I'm left with more questions than I started with and now I have to burn more time trying to make sense of the notes I just took. That's not even considering that 50% of the time when they get me on the call there's a "oh by the way since you're here can you do this project as well". This has the effect of disincentivizing me from seeking guidance. Furthermore, I never actually get projects over the finish line because every time I pass off my results there's millions of changes and updates that I'm asked to do. I used to be a very proactive person in school and in more junior jobs, I used to get things done ahead of time. But not anymore, If I finish a project ahead of time they'll just scope creep it to death, vs if I just sit on it and pass it off right before the deadline, they'll be forced to accept that it's good enough and just take it. I'm also being disincentivized to work efficiently. The biggest part of my job is stenography. I'm not even exaggerating. I know you guys are going to say it sounds like a culture problem, but it has been like this in the last 3 DS positions I've had at different companies. As I said, I think the root of the problem is that the stakeholders are strapped for time, but in a world of "streamlining headcount", I don't really see that changing. If this thread is popular, know I'm gonna get a bunch of people hijacking it ask for advice for getting into the field. See my comment here: https://www.reddit.com/r/datascience/comments/1e951vk/comment/lfcvrof/ Please don't ask me how to get into this field unless you've read this comment and have a question on something that I specifically didn't address in it. submitted by /u/son_of_tv_c [link] [comments]
Hi everyone, I’m the creator of www.DataScienceHive.com, a platform dedicated to providing free and accessible learning paths for anyone interested in data analytics, data science, and related fields. The mission is simple: to help people break into these careers with high-quality, curated resources and a supportive community. We also have a growing Discord community with over 50 members where we discuss resources, projects, and career advice. You can join us here: https://discord.gg/FYeE6mbH. I’m excited to announce that I’ve just finished building the “Data Analyst Learning Path”. This is the first version, and I’ve spent a lot of time carefully selecting resources and creating homework for each section to ensure it’s both practical and impactful. Here’s the link to the learning path: https://www.datasciencehive.com/data_analyst_path Here’s how the content is organized: Module 1: Foundations of Data Analysis • Section 1.1: What Does a Data Analyst Do? • Section 1.2: Introduction to Statistics Foundations • Section 1.3: Excel Basics Module 2: Data Wrangling and Cleaning / Intro to R/Python • Section 2.1: Introduction to Data Wrangling and Cleaning • Section 2.2: Intro to Python & Data Wrangling with Python • Section 2.3: Intro to R & Data Wrangling with R Module 3: Intro to SQL for Data Analysts • Section 3.1: Introduction to SQL and Databases • Section 3.2: SQL Essentials for Data Analysis • Section 3.3: Aggregations and Joins • Section 3.4: Advanced SQL for Data Analysis • Section 3.5: Optimizing SQL Queries and Best Practices Module 4: Data Visualization Across Tools • Section 4.1: Foundations of Data Visualization • Section 4.2: Data Visualization in Excel • Section 4.3: Data Visualization in Python • Section 4.4: Data Visualization in R • Section 4.5: Data Visualization in Tableau • Section 4.6: Data Visualization in Power BI • Section 4.7: Comparative Visualization and Data Storytelling Module 5: Predictive Modeling and Inferential Statistics for Data Analysts • Section 5.1: Core Concepts of Inferential Statistics • Section 5.2: Chi-Square • Section 5.3: T-Tests • Section 5.4: ANOVA • Section 5.5: Linear Regression • Section 5.6: Classification Module 6: Capstone Project – End-to-End Data Analysis Each section includes homework to help apply what you learn, along with open-source resources like articles, YouTube videos, and textbook readings. All resources are completely free. Here’s the link to the learning path: https://www.datasciencehive.com/data_analyst_path Looking Ahead: Help Needed for Data Scientist and Data Engineer Paths As a Data Analyst by trade, I’m currently building the “Data Scientist” and “Data Engineer” learning paths. These are exciting but complex areas, and I could really use input from those with strong expertise in these fields. If you’d like to contribute or collaborate, please let me know—I’d greatly appreciate the help! I’d also love to hear your feedback on the Data Analyst Learning Path and any ideas you have for improvement. submitted by /u/Ryan_3555 [link] [comments]
Looking at the current market trends, what skills do you think one should focus on to land an entry level data analyst/data science job in 8-9 months? Portfolio building, networking and preparing for interviews is already assumed but ... Our time is limited. We cannot learn and focus on everything. What skills might be best spend on to land a job within this timeframe. My educational background: Bachelor of Computing in Information Systems Currently persuing Msc Data Science and Computational Intelligence. (9 months left to graduate). All courses are finished, just the thesis left. My professional background: Have experience as a content writer, content editor, technical writer etc. Have done an 8 week Software Engineering internship (focused on fullstack JS/TS stack.) Have done 2 months Internship as a "Data Science intern" but it was focused on web scraping, cleaning data obtained through an API to generate market leads, building proof of concept LLM applications using Langchain and Google Gemini/OpenAI API keys. Note: I'm from a 3rd world country. I cannot offer you any financial compensation for your detailed guided response even if I really want to (unless it is in Nrs). So, please ignore this post, it you are looking for monetary reward for you high quality response. Please don't ask me to look at job postings, ask ChatGPT, Google. I've done those things. Job descriptions are like wishlists. If I read a JD, I come up with an impression that I need to have 10 year internship experience with almost every technology imaginable just to land an entry level job. Provide me with your personal perspective. submitted by /u/httpsdash [link] [comments]
As my work for the coming year is coming into focus, there is a heavy emphasis on building customer-facing ETL pipelines and dashboards. My team has chosen PowerBI as its dashboarding application of choice. Compared to building a web-app based dashboard with plotly dash or the like, making PowerBI dashboards is AGONIZING. I'm able to do most data transformations with SQL beforehand, but having to use powerquery or god forbid DAX for a viz-specific transformation feels like getting a root canal. I can't stand having to click around Microsoft's shitty UI to create plots that I could whip up in a few lines of code. I'm strongly considering looking for a new opportunity and jumping ship solely to avoid having to work with PowerBI. I'm also genuinely concerned about my technical skills decaying while other folks on my team get to continue working on production models and genAI hotness. Anyone been in a similar situation? How did you handle it? TLDR: python-linux-sql data scientist being shoehorned into no-code/PowerBI, hates life submitted by /u/Smarterchild1337 [link] [comments]
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