# 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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• Bayes' rule usage
by /u/TheFilteredSide (Data Science) on May 27, 2024 at 7:08 am

I heard that Bayes' rule is one of the most used , but not spoken about component by many Data scientists. Can any one tell me some practical examples of where you are using them ? submitted by /u/TheFilteredSide [link] [comments]

• So have a upcoming take home task for a data insights role - one option is to present something that I have done before to demonstrate ability to draw insights. Is this too far left field??
by /u/damjanv1 (Data Science) on May 27, 2024 at 4:45 am

• Weekly Entering & Transitioning - Thread 27 May, 2024 - 03 Jun, 2024
by /u/AutoModerator (Data Science) on May 27, 2024 at 4:01 am

Welcome to this week's entering & transitioning thread! This thread is for any questions about getting started, studying, or transitioning into the data science field. Topics include: Learning resources (e.g. books, tutorials, videos) Traditional education (e.g. schools, degrees, electives) Alternative education (e.g. online courses, bootcamps) Job search questions (e.g. resumes, applying, career prospects) Elementary questions (e.g. where to start, what next) While you wait for answers from the community, check out the FAQ and Resources pages on our wiki. You can also search for answers in past weekly threads. submitted by /u/AutoModerator [link] [comments]

• [D] need help with a seemingly easy interview questions!
by /u/zolkida (Machine Learning) on May 26, 2024 at 11:42 pm

In short, I received this question during interviews six months ago. It was in an asynchronous video interview, so I didn't get a chance for a back and forth, but these are the exact words. "You have a multiple linear regression model used for classification that is performing poorly. You have ruled out insufficient data, imbalanced classes, no signal in the data, and you have checked for a linear relationship Please describe what other statistical problems may be affecting the performance of the model." I'm not sure if this is legit, or if the interviewer is trying to get me to discover the bug he was facing by some form of telepathy. I don't have a satisfying answer, and I'm not well versed in statistics. So I want to see how you would answer it. submitted by /u/zolkida [link] [comments]

• [P] RAGoon : Improve Large Language Models retrieval using dynamic web-search
by /u/louisbrulenaudet (Machine Learning) on May 26, 2024 at 10:24 pm

RAGoon thumbnail. RAGoon is a Python library that aims to improve the performance of language models by providing contextually relevant information through retrieval-based querying, web scraping, and data augmentation techniques. It offers an integration of various APIs, enabling users to retrieve information from the web, enrich it with domain-specific knowledge, and feed it to language models for more informed responses. RAGoon's core functionality revolves around the concept of few-shot learning, where language models are provided with a small set of high-quality examples to enhance their understanding and generate more accurate outputs. By curating and retrieving relevant data from the web, RAGoon equips language models with the necessary context and knowledge to tackle complex queries and generate insightful responses. Usage Example Here's an example of how to use RAGoon : from groq import Groq # from openai import OpenAI from ragoon import RAGoon # Initialize RAGoon instance ragoon = RAGoon( google_api_key="your_google_api_key", google_cx="your_google_cx", completion_client=Groq(api_key="your_groq_api_key") ) # Search and get results query = "I want to do a left join in python polars" results = ragoon.search( query=query, completion_model="Llama3-70b-8192", max_tokens=512, temperature=1, ) # Print results print(results)  Key Features Query Generation : RAGoon generates search queries tailored to retrieve results that directly address the user's intent, enhancing the context for subsequent language model interactions. Web Scraping and Data Retrieval : RAGoon leverages web scraping capabilities to extract relevant content from various websites, providing language models with domain-specific knowledge. Parallel Processing : RAGoon utilizes parallel processing techniques to efficiently scrape and retrieve data from multiple URLs simultaneously. Language Model Integration : RAGoon integrates with language models, such as OpenAI's GPT-3 or LLama 3 on Groq Cloud, enabling users to leverage natural language processing capabilities for their applications. Extensible Design : RAGoon's modular architecture allows for the integration of new data sources, retrieval methods, and language models, ensuring future extensibility. Link to GitHub : https://github.com/louisbrulenaudet/ragoon submitted by /u/louisbrulenaudet [link] [comments]

• [R] (RL) Relation between environment complexity and optimal policy convergence
by /u/Main_Pressure271 (Machine Learning) on May 26, 2024 at 10:23 pm

Hey guys, is there some literature on the relationship between the complexity of the environment, and the learned optimal policy itself ? For example, if an environment is generated by a VAE in “world model”, what’s the relation between the environment complexity and policy ? submitted by /u/Main_Pressure271 [link] [comments]

• Building models with recruiting data
by /u/Understands-Irony (Data Science) on May 26, 2024 at 8:33 pm

Hello! I recently finished a Masters in CS and have an opportunity to build some models with recruiting data. I’m a little stuck on where to start however - I have lots of data about individual candidates (~100k) and lots of jobs the company has filled and is trying to fill. Some models I’d like to make: Based on a few bits of data about the open role (seniority, stage of company, type of role, etc.), how can I predict which of our ~100K candidates would be a fit for it? My idea is to train a model based on past connections between candidates and jobs, but I’m not sure how to structure the data exactly or what model to apply to it. Any suggestions? Another, simpler problem: I’m interested in clustering roles to identify which are similar based on the seniority/function/industry of the role and by the candidates attached to them. Is there a good clustering algorithm I should use and method of visualizing this? Also, I’m not sure how to structure data like a list of candidate_ids. If this isn’t the right forum / place to ask this, I’d appreciate suggestions! submitted by /u/Understands-Irony [link] [comments]

• Do you use feature transformations in real world (ranking, sqrt, log etc.)?
by /u/maybenexttime82 (Data Science) on May 26, 2024 at 7:38 pm

I understand their usage and that the models can greatly benefit from them (they can help models better capture "hidden" nonlinearities, help with outliers etc.), but since I am not working in the field yet my concern is that when you communicate with stakeholders do you report that you were using those? Say you have tabular data and doing simple linear regression model. submitted by /u/maybenexttime82 [link] [comments]

• [D] Chinese text such as Genesis meticulously translated to have the exact same semantic meaning as the English but takes up half the memory. Would training LLM using Chinese be more efficient due to higher semantic density per byte?
by /u/Civil_Repair (Machine Learning) on May 26, 2024 at 4:25 pm

• [P] ReRecall: I tried to recreate Microsoft's Recall using open-source models & tools
by /u/Abdoo2 (Machine Learning) on May 26, 2024 at 4:08 pm

Recall sounds to me like a privacy nightmare, so I thought I might give it a try to make something similar using only open source components. Here is the code if you want to play around with it: https://github.com/AbdBarho/ReRecall Overall it went better than I expected, I use mss` to take screenshots of the monitor(s), and use ollama and llava and mxbai embed to generate descriptions and embeddings of the screenshots, and then chromadb for storage and search. There is definitely huge room for improvement here: There are plenty of hallucinations in the generated descriptions of screenshots, this could be a combination of the size the MLLM used to generate the descriptions (I use a very small model because I have a rusty 1060), or because the screenshots are very high in resolutions (no resizing is done after a screenshot). The search is very basic, it just matches the embeddings of the query text with the embeddings of the screenshots, a potential improvement could be to use the model to enrich the user query with more information before embedding it for search. I am fairly certain that Microsoft does not rely solely on screenshots as I do, but also captures of individual app windows, and also extracts meta information like window title, maybe even the text content of the window (the same text used by text-to-speech programs for the visually impaired), these could definitely improve the results. Do you have any further ideas on what could be changed? Example (cherrypicked): Screen on the right with the corresponding ReRecall usage on the left submitted by /u/Abdoo2 [link] [comments]

• Multiple-outputs regression
by /u/Rich-Effect2152 (Data Science) on May 26, 2024 at 1:14 pm

I am a data scientist working in the renewable energy industry, specializing in photovoltaic power generation forecasting. Every morning at 7:00 AM, I need to predict the photovoltaic power output for 96 points for the next day. Why 96 points? Because there is a forecast value every 15 minutes. Previously, I used a LightGBM model, where I would first calculate features and then invoke the model for each 15-minute interval. Essentially, this involved calling the model 96 times since these 96 points are independent in the forecasting process. Now, I want to develop a multiple-outputs model that treats the power values of these 96 points as 96 columns of labels. After researching, I found that I could use the CatBoost model for this purpose. Do you think this method is feasible? Or is there a better approach? submitted by /u/Rich-Effect2152 [link] [comments]

• [P] MOMENT: A Foundation Model for Time Series Forecasting, Classification, Anomaly Detection and Imputation
by /u/apaxapax (Machine Learning) on May 26, 2024 at 12:46 pm

• [R] Why In-Context Learning Transformers are Tabular Data Classifiers
by /u/FelixdenBreejen (Machine Learning) on May 26, 2024 at 8:09 am

We are introducing TabForestPFN, which is an in-context learning transformer that can predict tabular data classification tasks. In the past, tabular data classification was dominated by tree-based algorithms like XGBoost and CatBoost, but now we are finally closing this gap using pretrained transformers. https://preview.redd.it/c3unlgi1cq2d1.png?width=2690&format=png&auto=webp&s=cd414509a31a189df288668e928d52e5723df3fc In-context learning transformers were introduced to tabular data classification by Hollman et al. (ICLR, 2023) in TabPFN. This work is limited by the GPU memory, so it only considers datasets with fewer than a thousand observations. We improve their model by adding a fine-tuning stage, which circumvents the GPU memory limitation. Also, we introduce an additional synthetic data forest generator to further boost the performance. The result is TabForestPFN. The focus of the TabForestPFN paper is about why we can pretrain on tabular data. In language and vision, pretraining can learn grammar and textures, so pretraining makes sense. But in tabular data, the datasets in pretraining share no features or labels with the real-world datasets of interest, so what could it even learn? In the paper, we argue in-context learning transformers learn the ability to create complex decision boundaries. If you are interested in the reasoning, give it a read. Code is available at https://github.com/FelixdenBreejen/TabForestPFN With the code, you can reproduce all our pretraining, experiments and analysis, and it also includes some basic examples for you to immediately use the classifier on your own datasets. Below are the results of TabForestPFN on two tabular data classification benchmarks. I am the author, so if there are any questions, feel free to ask. https://preview.redd.it/1tavhybhzq2d1.png?width=1174&format=png&auto=webp&s=214fb394a229544dfd8b44677d7880852c5d222f https://preview.redd.it/9tg9z9tobq2d1.png?width=832&format=png&auto=webp&s=9fd3c732be8d5e18c8f56bb2b0e1c94796968056 submitted by /u/FelixdenBreejen [link] [comments]

• [D] ML paper verb tense
by /u/cosmoquester (Machine Learning) on May 26, 2024 at 7:23 am

Why do most ML papers use all verb tenses in the present tense like MLA format while using a citation style or reference section as APA style? In particular, even though academic societies such as ICML explicitly say that they follow the APA style, most of the papers' verb tenses do not seem to be followed by instructions in the APA guide to write the past, present, and future appropriately. submitted by /u/cosmoquester [link] [comments]

• [Discussion] Prediction Models for multi-tenant system in finance sector
by /u/Puzzleheaded-Rest734 (Machine Learning) on May 26, 2024 at 7:20 am

Let's suppose a finance SaaS platform with 100 million customers wants to introduce a sales prediction service. How would one design a system that... Predicts sales forecast based on historical data of each tenant Will it entail training and building 100 million models ( model per tenant) Any guidance here is appreciated. Also, any blog/reference material to read about such design case studies would be helpful. Thanks submitted by /u/Puzzleheaded-Rest734 [link] [comments]

• [D] Specific to ViT(visual transformers) are there any learnable params in patch embeddings?
by /u/elongatedpepe (Machine Learning) on May 26, 2024 at 7:13 am

I'm trying to understand where exactly in ViT are the learnable parameters. First step is to convert patch to patch embeddings to feed into n/w so we add a simple linear transformation (FCN) for dims reduction and matrix->vector. What is learnt here? Are there any weights? Or is it just shrinking the 2d patch input to a 1d vector. Since these patches are processed(linear transformed) in parallel, they have no idea on other patch information. People say patch to patch interaction happen in attention layer BUT there are no learnable params in attention layer it's just transpose and multiple query key patch. Does the backprop in attention layer loss cause weights to change in patch embedding layer?? Also, why do they call as linear transformation of patch embedding? Aren't they adding any activation function, it's supposed to be non linear transformation right? submitted by /u/elongatedpepe [link] [comments]

• [R] Testing theory of mind in large language models and humans
by /u/AhmedMostafa16 (Machine Learning) on May 26, 2024 at 6:44 am

• [R] [CVPR 2024] AV-RIR: Audio-Visual Room Impulse Response Estimation
by /u/Snoo63916 (Machine Learning) on May 26, 2024 at 4:26 am

• [D] Can Image to Image Diffusion bridges models be used to solve Image segmentation problems?
by /u/Far-Theory-7027 (Machine Learning) on May 25, 2024 at 9:15 pm

Can Image to Image Diffusion bridges like BBDM:Image-to-image Translation with Brownian Bridge Diffusion Models be used to solve Image segmentation problems? submitted by /u/Far-Theory-7027 [link] [comments]

• [D] What's the best way for me to go about building a robust yet human-like playable Poker AI Model
by /u/HandfulOfAStupidKid (Machine Learning) on May 25, 2024 at 7:50 pm

I'm working on a (Texas hold 'em) Poker game and I'd like to have an AI that can play at a human-ish level. I've developed a win probability calculator which can find the odds of you having the best hand in the game given your cards, the community cards, and the number of players in the game. I'm unsure of where to go from here. I study ML/AI in school but I've been having a hard time making the best decision on how to actually apply these tools in practice. Firstly, I'm unsure of what dataset to use, I found a dataset of online poker game logs which might useful. Also, I don't know whether to develop a decision tree, use neural networks, or a combination of the two and/or other methods. What's the best way to go about building my AI model using ML for this project? submitted by /u/HandfulOfAStupidKid [link] [comments]

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