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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:
| 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
$$ \operatorname {Cov} (X,Y)=\sum _{i=1}^{n}\left({x_{i}}-{\bar {x}}\right)\left({y_{i}}-{\bar {y}}\right) $$
For our sales example, that calculation would look like this:
$$ \operatorname {Var} (Y)=\sum _{i=1}^{3}\left({y_{i}}-{\bar {y}}\right)^{2}=(100-150)^{2}+(150-150)^{2}+(200-150)^{2})=2500 $$
and
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$$ \operatorname {Cov} (X,Y)=\sum _{i=1}^{3}\left({x_{i}}-{\bar {x}}\right)\left({y_{i}}-{\bar {y}}\right)=(2016-2017)(100-150)+(2017-2017)(150-150)+(2018-2017)(200-150))=-500 $$
Now we can finally calculate our autoregressive parameters! We do that by solving this equation:
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$$ \hat {\beta }=(X^{\prime }X)^{-1}X^{\prime }Y=\frac {1}{2500}\times 2500\times (-500)=0.20 $$\.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.
Continue reading | Check out the paper and github link.
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Hi. I am not sure whether this is the right subreddit, but I want to write it here. I am a student and starting my research project. I just want to use any two pre-trained models that is existing like ClinicalBert, Biobert and to showcase the comparison. Hence, I don't want or need to do any fine tuning. Only want to implement into my system, run the chatbot and have a conversation with it. it would really be helpful if someone can help me on suggesting any good pre-trained medical chatbot usable models submitted by /u/Apstyles_17 [link] [comments]
- [D] CVPR 2025 Reviews are out!! How did it go?by /u/ElPelana (Machine Learning) on January 22, 2025 at 6:36 pm
I got a Reject (1), Borderline (3) and Accept (5), with confidence (3,3,4)! Quite stochastic I'd say!! But the Reject reviewer is not quite bad actually. submitted by /u/ElPelana [link] [comments]
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- Scrapy MRO error without any references to conflicting packagesby /u/Tamalelulu (Data Science) on January 22, 2025 at 3:55 pm
Hi all, I'm working on a little personal project, quantifying what technologies are most asked for in Data Science JDs. Really I'm more using it to work on my Python chops. I'm hitting a slightly perplexing error and I think ChatGPT has taken me as far as it possibly can on this one. When I attempt to crawl my spider I get this error: TypeError: Cannot create a consistent method resolution order (MRO) for bases Injectable, Generic Previously the code was attempting to import Injectable from scrap_poet until I eventually inspected the package and saw that Injectable doesn't exist. So I attempted to avoid using that entirely and omitted all references to Injectable in my code. Yet I'm still getting this error. Any thoughts? Here's what the spider looks like: import scrapy import csv from scrapy_autoextract import request_raw class JobSpider(scrapy.Spider): name = "job_spider" custom_settings = { "DOWNLOADER_MIDDLEWARES": { "scrapy_autoextract.AutoExtractMiddleware": 543, }, } # Read URLs from links.csv and start requests def start_requests(self): with open("/adzuna_links.csv", "r") as file: reader = csv.reader(file) for row in reader: url = row[0] yield request_raw(url=url, page_type="jobposting", callback=self.parse) def parse(self, response): try: # Extract job details directly from the response JSON data returned by AutoExtract job_data = response.json().get("job_posting", {}) if job_data: yield { "title": job_data.get("title"), "description": job_data.get("description"), "company": job_data.get("hiringOrganization", {}).get("name"), "location": job_data.get("jobLocation", {}).get("address"), "datePosted": job_data.get("datePosted"), } else: self.logger.error(f"No job data extracted from {response.url}") except Exception as e: self.logger.error(f"Error parsing job data from {response.url}: {e}") submitted by /u/Tamalelulu [link] [comments]
- [D] CVPR 2025 Reviewsby /u/Some-Landscape-4763 (Machine Learning) on January 22, 2025 at 3:31 pm
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This paper presents an approach for learning world knowledge directly from unlabeled video data through a self-supervised framework called VideoWorld. The core technical contribution is a multi-stage architecture that processes videos to extract both visual and temporal relationships without requiring manual annotation. Key technical points: - Uses contrastive learning between video segments to capture temporal dynamics - Implements cross-modal alignment between visual and motion features - Employs temporal consistency learning to understand event sequences - Introduces a hierarchical attention mechanism for long-range dependencies Results demonstrate improvement over existing methods: - 12% increase in video QA performance on HowTo100M - 15% better temporal relationship understanding on ActivityNet - 8% improvement in next-frame prediction tasks - Effective zero-shot transfer to unseen video domains I think this approach could significantly change how we train video understanding models. By removing the need for expensive manual labeling, we could potentially train on much larger and more diverse video datasets. I'm particularly interested in how this could improve robotic learning systems that need to understand physical interactions and causality. The results suggest good potential for real-world applications, though I think there are still important challenges around computational efficiency and handling of abstract concepts that need to be addressed. TLDR: New self-supervised framework learns world knowledge from unlabeled videos, showing strong improvements on video understanding tasks without requiring manual annotations. Full summary is here. Paper here. submitted by /u/Successful-Western27 [link] [comments]
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- Practices of an Agile Developer
- Don't Make Me Think
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- The Design of Everyday Things by Donald Norman
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- Best Software Writing I by Joel Spolsky
- The Practice of Programming by Kernighan and Pike
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- Software Estimation: Demystifying the Black Art by Steve McConnel
- The Passionate Programmer (My Job Went To India) by Chad Fowler
- Hackers: Heroes of the Computer Revolution
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- JavaScript - The Good Parts
- Getting Real by 37 Signals
- Foundations of Programming by Karl Seguin
- Computer Graphics: Principles and Practice in C (2nd Edition)
- Thinking in Java by Bruce Eckel
- The Elements of Computing Systems
- Refactoring to Patterns by Joshua Kerievsky
- Modern Operating Systems by Andrew S. Tanenbaum
- The Annotated Turing
- Things That Make Us Smart by Donald Norman
- The Timeless Way of Building by Christopher Alexander
- The Deadline: A Novel About Project Management by Tom DeMarco
- The C++ Programming Language (3rd edition) by Stroustrup
- Patterns of Enterprise Application Architecture
- Computer Systems - A Programmer's Perspective
- Agile Principles, Patterns, and Practices in C# by Robert C. Martin
- Growing Object-Oriented Software, Guided by Tests
- Framework Design Guidelines by Brad Abrams
- Object Thinking by Dr. David West
- Advanced Programming in the UNIX Environment by W. Richard Stevens
- Hackers and Painters: Big Ideas from the Computer Age
- The Soul of a New Machine by Tracy Kidder
- CLR via C# by Jeffrey Richter
- The Timeless Way of Building by Christopher Alexander
- Design Patterns in C# by Steve Metsker
- Alice in Wonderland by Lewis Carol
- Zen and the Art of Motorcycle Maintenance by Robert M. Pirsig
- About Face - The Essentials of Interaction Design
- Here Comes Everybody: The Power of Organizing Without Organizations by Clay Shirky
- The Tao of Programming
- Computational Beauty of Nature
- Writing Solid Code by Steve Maguire
- Philip and Alex's Guide to Web Publishing
- Object-Oriented Analysis and Design with Applications by Grady Booch
- Effective Java by Joshua Bloch
- Computability by N. J. Cutland
- Masterminds of Programming
- The Tao Te Ching
- The Productive Programmer
- The Art of Deception by Kevin Mitnick
- The Career Programmer: Guerilla Tactics for an Imperfect World by Christopher Duncan
- Paradigms of Artificial Intelligence Programming: Case studies in Common Lisp
- Masters of Doom
- Pragmatic Unit Testing in C# with NUnit by Andy Hunt and Dave Thomas with Matt Hargett
- How To Solve It by George Polya
- The Alchemist by Paulo Coelho
- Smalltalk-80: The Language and its Implementation
- Writing Secure Code (2nd Edition) by Michael Howard
- Introduction to Functional Programming by Philip Wadler and Richard Bird
- No Bugs! by David Thielen
- Rework by Jason Freid and DHH
- JUnit in Action
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Top 1000 Canada Quiz and trivia: CANADA CITIZENSHIP TEST- HISTORY - GEOGRAPHY - GOVERNMENT- CULTURE - PEOPLE - LANGUAGES - TRAVEL - WILDLIFE - HOCKEY - TOURISM - SCENERIES - ARTS - DATA VISUALIZATION
Top 1000 Africa Quiz and trivia: HISTORY - GEOGRAPHY - WILDLIFE - CULTURE - PEOPLE - LANGUAGES - TRAVEL - TOURISM - SCENERIES - ARTS - DATA VISUALIZATION
Exploring the Pros and Cons of Visiting All Provinces and Territories in Canada.
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Health Health, a science-based community to discuss human health
- Scientists in Italy discover rare gene that could cause Alzheimer’sby /u/euronews-english on January 22, 2025 at 1:49 pm
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- Childhood Vaccination Rates Continue to Slipby /u/Generalaverage89 on January 22, 2025 at 1:20 pm
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- Trump’s Plan to Leave the WHO Is a Health Disasterby /u/wiredmagazine on January 22, 2025 at 11:17 am
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- FDA allows standalone use of nasal spray antidepressant Spravato (esketamine)by /u/Maxcactus on January 22, 2025 at 10:35 am
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- Eating too much red meat linked to an increased risk of dementia and cognitive declineby /u/euronews-english on January 22, 2025 at 9:49 am
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Today I Learned (TIL) You learn something new every day; what did you learn today? Submit interesting and specific facts about something that you just found out here.
- TIL the T4 Program was a Nazi German euthanasia program that forcibly killed the physically or mentally disabled, the emotionally distraught, elderly people and the incurably ill. The death toll may have reached 200,000 or moreby /u/wilsonofoz on January 22, 2025 at 2:19 pm
submitted by /u/wilsonofoz [link] [comments]
- TIL that inventors of the two most impactful weapon technologies of WWII, Merle Tuve (proximity fuse) and Ernest Lawrence (uranium enrichment for the atomic bomb) were childhood friends and neighbors from the same small town in South Dakotaby /u/JiveChicken00 on January 22, 2025 at 1:38 pm
submitted by /u/JiveChicken00 [link] [comments]
- TIL that there is a species of whale that has been living in the oceans for millions of years, but it was only recently discovered due to its isolation in the deep depths.by /u/QuietKnightX on January 22, 2025 at 10:13 am
submitted by /u/QuietKnightX [link] [comments]
- TIL In the Netherland a town exists that fully encloses 22 small exclaves of a Belgian town.by /u/Bangfis on January 22, 2025 at 10:08 am
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- TIL that a huge 20m (66ft) rogue wave hit the bulk carrier, MV Derbyshire with such force that it sent the ship underwater almost instantly, not even giving its crew enough time to save themselves, let alone send a distress signal.by /u/zahrul3 on January 22, 2025 at 9:10 am
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Reddit Science This community is a place to share and discuss new scientific research. Read about the latest advances in astronomy, biology, medicine, physics, social science, and more. Find and submit new publications and popular science coverage of current research.
- Black immigrants attract white residents to neighborhoods, while native Black residents move out, study finds.by /u/geoff199 on January 22, 2025 at 1:24 pm
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- Antibiotics, antivirals and vaccines could help tackle dementia, study suggests. Using drugs approved for other conditions could dramatically speed up hunt for cure, experts say.by /u/mvea on January 22, 2025 at 12:10 pm
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- Study links early emotional regulation difficulties to ADHD and conduct problems | The findings highlight the importance of early emotional development and could guide targeted support for children at risk.by /u/chrisdh79 on January 22, 2025 at 11:02 am
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- Researchers have discovered that proteins in the mollusk’s blood not only have bacteria-killing properties, raising the possibility of a new antibiotic, but also increase the effectiveness of some existing antibiotics.by /u/chrisdh79 on January 22, 2025 at 10:59 am
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- A new study highlights how scaling up COVID-19 testing in the USA saved an estimated 1.4 million lives and averted 7 million hospitalisations. It emphasises the vital role of rapid testing in reducing severe outcomes and preparing for future pandemics.by /u/calliope_kekule on January 22, 2025 at 10:22 am
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Reddit Sports Sports News and Highlights from the NFL, NBA, NHL, MLB, MLS, and leagues around the world.
- NFL news roundup: Saints rescheduling HC interviews due to severe weatherby /u/EvelynClede on January 22, 2025 at 7:33 am
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- 4 arrested in connection with burglary at Joe Burrow's houseby /u/Oldtimer_2 on January 22, 2025 at 4:01 am
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- Madison Keys reaches the Australian Open semifinals with a win over Elina Svitolinaby /u/Oldtimer_2 on January 22, 2025 at 3:52 am
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- Ichiro Suzuki, CC Sabathia and Billy Wagner elected to Baseball Hall of Fameby /u/Oldtimer_2 on January 22, 2025 at 12:27 am
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- Young collector nabs rare Paul Skenes card that could offer him a hefty haul in trade with Piratesby /u/Oldtimer_2 on January 22, 2025 at 12:16 am
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