# 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).

## Finding Autoregressive Parameters: The Math Behind ItTo 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:

| Year | Sales |
|——|——-|
| 2016 | 100 |
| 2017 | 150 |
| 2018 | 200 |

Next, you need to calculate the means for each column. For our sales example, that would look like this:

$$\bar{Y} = \frac{100+150+200}{3} = 150$$

Now we can calculate each element in what’s called the variance-covariance matrix:

$$\operatorname {Var} (X)=\sum _{i=1}^{n}\left({x_{i}}-{\bar {x}}\right)^{2}$$

and

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$$\operatorname {Cov} (X,Y)=\sum _{i=1}^{n}\left({x_{i}}-{\bar {x}}\right)\left({y_{i}}-{\bar {y}}\right)$$

For our sales example, that calculation would look like this:

$$\operatorname {Var} (Y)=\sum _{i=1}^{3}\left({y_{i}}-{\bar {y}}\right)^{2}=(100-150)^{2}+(150-150)^{2}+(200-150)^{2})=2500$$

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and

$$\operatorname {Cov} (X,Y)=\sum _{i=1}^{3}\left({x_{i}}-{\bar {x}}\right)\left({y_{i}}-{\bar {y}}\right)=(2016-2017)(100-150)+(2017-2017)(150-150)+(2018-2017)(200-150))=-500$$

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Now we can finally calculate our autoregressive parameters! We do that by solving this equation:

$$\hat {\beta }=(X^{\prime }X)^{-1}X^{\prime }Y=\frac {1}{2500}\times 2500\times (-500)=0.20$$\.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.

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# Autoregressive Model

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.

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• Need Help with the Project.
by /u/wanderingblade04 (Data Science) on April 18, 2024 at 9:03 am

First of all Thanks to the sub members who gave me karma to post here. We are working on a project where we should find the percentage of similarilty between two texts using an LLM. Now what are all the LLMs that I can use? Any Idea lead would be helpful submitted by /u/wanderingblade04 [link] [comments]

• Restructuring in Big Tech
by /u/pintora0318 (Data Science) on April 18, 2024 at 6:49 am

Does anybody have any tips on how to handle re organization/ re-structuring? Still employed as DA. And tbh have avenues to stay at my company but seems like they’re moving to a more centralized data structure. Probably will give primary access to tech hub office employees. I am remote. I do power BI, vba and data processing. Right now mostly ETL stuff. Any tips would be appreciated! submitted by /u/pintora0318 [link] [comments]

• Learning OOP, stick with Python or learn using Java
by /u/orndoda (Data Science) on April 18, 2024 at 2:37 am

I’m starting a Master’s program in the fall and I’d like to improve my programming skills. My undergrad was in Math, so programming wasn’t really much of a focus. I took one actual CS course which mostly used Python and just a little bit of C. I encountered R in college in my Stats courses and I use it regularly in my current role (DBA/Analyst at a small nonprofit). I’ve also kept up with Python and I’m fairly comfortable with it still. I’ve never actually learned about OOP or say structures and algorithms but I’d like to. I’ve read a bunch about Java being a more rigorous language which forces you to code in an object-oriented way. I guess my question is: is there enough of a benefit to using Java for OOP, or should I just use resources designed for Python? submitted by /u/orndoda [link] [comments]

• Is freelance data science a thing?
by /u/trashed_culture (Data Science) on April 17, 2024 at 11:56 pm

If anyone has any experiences, I'd love to hear it. And if it's not a thing, what are the blockers in your opinion? submitted by /u/trashed_culture [link] [comments]

• Job hunt update.
by /u/JeepMan831 (Data Science) on April 17, 2024 at 11:54 pm

I made this post after getting an offer a couple months ago. A couple weeks after the offer, it was rescinded. Probably for the best as I realized the original description did not match the actual role. After the offer was rescinded, I took a couple weeks off the job hunt before getting back at it. Cleaned up the resume, started being more selective with where I applied, and grinding SQL problems online. About a month in I was interviewing with 3 companies. I don't feel like making another Sankey, but it's pretty much identical to the last, except I got 3 first round interviews, rather than the 1 last time. Companies are 1 mid-sized tech and 2 pre-IPO unicorns. I was ghosted by one unicorn after a screening round and am still interviewing with the other after 2 rounds, though after 5 rounds with the mid-sized tech I accepted a DS manager position. My advice: 1) stop following this subreddit, it's 90% doom posting and 10% circle jerk. It doesn't feel like anyone here is actually interested in data science beyond getting a job. 2) mass send an easy to parse resume everywhere. 3) keep your head up, it's a grind. Don't forget to exercise, eat well, and have a social outlet. 4) referrals aren't worth what they once were. None of my dozen or so referrals resulted in even a screening interview I was rejected for roles I thought I was a shoo-in for and interviewed for roles I thought were a reach. There's a lot of luck (preparation+opportunity) involved that's often out of your control. Good luck submitted by /u/JeepMan831 [link] [comments]

• Preparation for a Final Round Interview for a Data Science Internship
by /u/deeht0xdagod (Data Science) on April 17, 2024 at 11:24 pm

Hello Everyone! This Friday, I have an upcoming final-round interview with the Director of the division I'd be interning under if I got the position. Per the recruiter, this is just to sort of solidify me as the right candidate for this role. I know that there won't be any sort of technical/coding aspect as it is just a 30-minute call. If anyone has any advice on how to approach it, it would be greatly appreciated! This is my first ever final round interview so any advice would be great! Thanks and have a great day! submitted by /u/deeht0xdagod [link] [comments]

• [N] Feds appoint “AI doomer” to run US AI safety institute
by /u/bregav (Machine Learning) on April 17, 2024 at 10:49 pm

https://arstechnica.com/tech-policy/2024/04/feds-appoint-ai-doomer-to-run-us-ai-safety-institute/ Article intro: Appointed as head of AI safety is Paul Christiano, a former OpenAI researcher who pioneered a foundational AI safety technique called reinforcement learning from human feedback (RLHF), but is also known for predicting that "there's a 50 percent chance AI development could end in 'doom.'" While Christiano's research background is impressive, some fear that by appointing a so-called "AI doomer," NIST may be risking encouraging non-scientific thinking that many critics view as sheer speculation. submitted by /u/bregav [link] [comments]

• [D] Is Risk Aversion Crushing the Adoption of Cloud Abstractions?
by /u/Ok_Post_149 (Machine Learning) on April 17, 2024 at 9:47 pm

Hey All, I think many of us can agree that defining the hardware we want to use right next to the piece of code we are running is objectively a much better developer experience. I have always loved the idea of lowering the barrier when it comes to running code in the cloud. As more cloud abstractions hit the market, I was honestly really surprised by the lack of adoption. There aren't any unicorns (I don't think any actually) in this space yet, just series A businesses. After speaking with a handful of Data Scientists, Machine Learning Engineers, and DevOps Engineers, it started to dawn on me that risk aversion is causing most of the friction. Using a fully managed service can definitely have some upsides, and in many cases, I prefer using them, but convincing your boss to pipe petabytes of data to another company's cloud and incur 3-5x compute costs probably isn't going to sit well. There are also some open source alternatives but they are intentionally difficult to configure so you pay for their premium offerings that reduce config setup. Would love to hear everyone's thoughts, especially those who work at lean startups and global 5,000 companies. submitted by /u/Ok_Post_149 [link] [comments]

• [Discussion] PhD in Statistics Job Prospects
by /u/SpiritualCellist4303 (Machine Learning) on April 17, 2024 at 8:59 pm

I am curious to know the job opportunities in Banking & Insurance for someone pursuing PhD in Statistics given the current market conditions. submitted by /u/SpiritualCellist4303 [link] [comments]

• [D] Is there a way to determine if the representations a model learns are spherical or hyperbolic?
by /u/Mad_Scientist2027 (Machine Learning) on April 17, 2024 at 8:49 pm

Title. Is there a way to determine the degree of sphericity or hyperbolicity of the embeddings a feature extractor learns for a set of examples it has been trained on / will be tested on? I am new to geometry in deep learning. It would be amazing if anyone could also point me to a paper or a book to get started on this. Thanks in advance. submitted by /u/Mad_Scientist2027 [link] [comments]

• [R] RuleOpt: Optimization-Based Rule Learning for Classification
by /u/zedeleyici3401 (Machine Learning) on April 17, 2024 at 7:34 pm

Paper: https://arxiv.org/abs/2104.10751 Package: https://github.com/sametcopur/ruleopt Documentation: https://ruleopt.readthedocs.io/ RuleOpt is an optimization-based rule learning algorithm designed for classification problems. Focusing on scalability and interpretability, RuleOpt utilizes linear programming for rule generation and extraction. The Python library ruleopt is capable of extracting rules from ensemble models, and it also implements a novel rule generation scheme. The library ensures compatibility with existing machine learning pipelines, and it is especially efficient for tackling large-scale problems. Here are a few highlights of ruleopt: Efficient Rule Generation and Extraction: Leverages linear programming for scalable rule generation (stand-alone machine learning method) and rule extraction from trained random forest and boosting models. Interpretability: Prioritizes model transparency by assigning costs to rules in order to achieve a desirable balance with accuracy. Integration with Machine Learning Libraries: Facilitates smooth integration with well-known Python libraries scikit-learn, LightGBM, and XGBoost, and existing machine learning pipelines. Extensive Solver Support: Supports a wide array of solvers, including Gurobi, CPLEX and OR-Tools. submitted by /u/zedeleyici3401 [link] [comments]

• [D] LSTM Time Series Forecasting
by /u/StressAccomplished26 (Machine Learning) on April 17, 2024 at 7:15 pm

I've been using LSTM models for time series forecasting and have noticed they perform well for predicting the immediate next step. However, when attempting multi-step predictions to forecast one week ahead (168 periods, with hourly data), the performance drops significantly. Currently, I'm using a recursive approach: feeding back the prediction as the next input (closed loop). This method isn't yielding good results, although open loop predictions are much more accurate. Is there a better technique for enhancing LSTM's multi-step prediction accuracy? Are LSTMs not useful for doing multi step forecasting? Any links or resources to articles explain multi step forecasting with LSTMs would be appreciated. https://preview.redd.it/30y3m16gr3vc1.png?width=833&format=png&auto=webp&s=6d6b29e05b105b50d2689127ea6881d1ec667903 https://preview.redd.it/a971j16gr3vc1.png?width=833&format=png&auto=webp&s=fec277d9343c5f702247a6135dbb630358c14cca submitted by /u/StressAccomplished26 [link] [comments]

• Suggestions for growth plan for a junior DS with one year experience
by /u/Florida-Rolf (Data Science) on April 17, 2024 at 6:35 pm

Hi, I'm one year into my first DS job at a big German company. I want to decide in which direction I want to develop myself careerwise and ask you for your opinion on that. Right now I do basic things like building ML models, big data analysis in pyspark, dashboards in powerbi and I also built small chatbots with streamlit, langchain and some Azure ressources. I know functional programming in Python but I never really learned object oriented programming, is this maybe something I should go for? I don't really have a senior colleague right now that could create a plan for me, it's a bit of a weird hierarchy there, so I'm super thankful for any input 🙂 Thank you! submitted by /u/Florida-Rolf [link] [comments]

• Using Data Science to Better Evaluate American Football Players
by /u/Data_Nerd1979 (Data Science) on April 17, 2024 at 6:19 pm

Dive into the transformative power of data science in the world of American football with Eric Eager, PhD's "Using Data Science to Better Evaluate American Football Players." In this presentation, Dr. Neubig, an expert in machine learning and natural language processing, showcases how the sport is evolving through advanced analytics. 🏈💻 From play-by-play and charting data to the revolutionary potential of player tracking data, discover the cutting-edge techniques that are setting the stage for a new era in football analysis. https://www.youtube.com/watch?v=8lwFUO_yj7c submitted by /u/Data_Nerd1979 [link] [comments]

• You know Gen AI != You know Deep Learning
by /u/Medium_Alternative50 (Data Science) on April 17, 2024 at 5:51 pm

Hi, I'm a student learning data science. I see few of my mates, making project with generative AI tools like langchain or open AI API etc But this is what I think, and I want to know if what I think is correct or not. Knowing how to use generative AI frameworks does not validate that you know deep learning or even basic machine learning. I think building projects with generative AI frameworks only validate that you know how to code by reading some docs. I think anyone who knows basic programming can make an "AI summarizer" or "AI Chatbot" using langchain. I don't feel that making such projects can make me standout in any way for machine learning jobs. I would rather make a basic data science project which at least tries to solve some real business problem. submitted by /u/Medium_Alternative50 [link] [comments]

• [R] ResearchAgent: Iterative Research Idea Generation over Scientific Literature with Large Language Models
by /u/SeawaterFlows (Machine Learning) on April 17, 2024 at 5:49 pm

Paper: https://arxiv.org/abs/2404.07738 Abstract: Scientific Research, vital for improving human life, is hindered by its inherent complexity, slow pace, and the need for specialized experts. To enhance its productivity, we propose a ResearchAgent, a large language model-powered research idea writing agent, which automatically generates problems, methods, and experiment designs while iteratively refining them based on scientific literature. Specifically, starting with a core paper as the primary focus to generate ideas, our ResearchAgent is augmented not only with relevant publications through connecting information over an academic graph but also entities retrieved from an entity-centric knowledge store based on their underlying concepts, mined and shared across numerous papers. In addition, mirroring the human approach to iteratively improving ideas with peer discussions, we leverage multiple ReviewingAgents that provide reviews and feedback iteratively. Further, they are instantiated with human preference-aligned large language models whose criteria for evaluation are derived from actual human judgments. We experimentally validate our ResearchAgent on scientific publications across multiple disciplines, showcasing its effectiveness in generating novel, clear, and valid research ideas based on human and model-based evaluation results. submitted by /u/SeawaterFlows [link] [comments]

• [R] Ctrl-Adapter: An Efficient and Versatile Framework for Adapting Diverse Controls to Any Diffusion Model
by /u/SeawaterFlows (Machine Learning) on April 17, 2024 at 5:34 pm

• [D] Question: Time-series decoding to non-temporal latent space?
by /u/reesespike (Machine Learning) on April 17, 2024 at 5:08 pm

Hello! I am a researcher in computational neuroscience, looking to apply some contemporary machine learning techniques to fMRI timeseries data. I have a collection of highly dimensional 4D fMRI timeseries data collected while subjects were observing naturalistic images from COCO at regular intervals. We currently have decoding models that take preprocessed "snapshots" of this timeseries data flattened into an activation pattern that is aggregated over the short period the image was being observed, and use some machine learning models to decode and reconstruct the image content from the brain. (See some of my recent work). I am curious what sort of machine learning techniques exist that might be able to address the time-series data itself, without having to collapse the timeseries to a single snapshot to perform our decoding process. What I am envisioning is a model (perhaps a transformer) that can take as input a highly dimensional multichannel timeseries and output a flattened latent representation (say, a CLIP vector) corresponding to an image stimulus, or even a series of latent vectors separated by a known regular interval (as we have in our data for the different image presentations). To my knowledge most of the work in machine learning with time series data is in forecasting, but what I want is a static (or potentially repetitive) output. My hope is that the more detailed timeseries data will have additional signal that will boost decoding performance for fMRI vision decoding. Is there any existing work in the field of ML that has tackled a similar problem? submitted by /u/reesespike [link] [comments]

• [D] Microsoft AutoML for ML.NET with DirectML
by /u/tradingnumbers (Machine Learning) on April 17, 2024 at 4:13 pm

I have built a model for detecting outliers in a data series using ML.NET. I read from the dev forums that ML.NET using DirectML can support the new NPUs built into the new Core Ultra processors from Intel. I have not been able to find evidence that this is true for AutoML from the Microsoft team. Does anyone have experience using AutoML with DirectML backend? submitted by /u/tradingnumbers [link] [comments]

• Is there some sort of multilevel KNN/ML model I can use to figure out which users will buy specific products?
by /u/Terrible-Hamster-342 (Data Science) on April 17, 2024 at 3:06 pm

I am wondering if there is some sort of multilevel model that I can use to identify likely buyers of specific products or create a lookalike audience. The issue is that I have 1000s of products and around a million users. It would be computationally infeasible to create a model for every product. The structure I am thinking of is the first level is a product and the next level is all the users in my database. Is there some sort of ML algo I could use to achieve this? submitted by /u/Terrible-Hamster-342 [link] [comments]

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