# 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.

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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:

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

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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:

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

and

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

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

$$\hat {\beta }=(X^{\prime }X)^{-1}X^{\prime }Y=\frac {1}{2500}\times 2500\times (-500)=0.20$$\.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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• [P] Computer Vision for package defects
by /u/aalwiz099 (Machine Learning) on April 23, 2024 at 4:44 pm

Hi, My team got a new project requirement.The ask is to develop a computer vision solution that can Identify the defects in inbound packages coming to a manufacturing warehouse. They come in fixed size pallets which contains multiple boxes. The defect could be anything - dents, torn packaging, broken pallet etc . How should I got about 1.Solution - GPT4 vision or custom trained models? Any recommendations from your experience in terms of model and training 2.Hardware requirements - how many cameras,what was your setup? Was latency a big issue? Any help would be greatly appreciated submitted by /u/aalwiz099 [link] [comments]

• [P] How can a project on fine-tuning an LLM as an artificial interviewer be made?
by /u/Holiday_Slip1271 (Machine Learning) on April 23, 2024 at 4:10 pm

I'm very new but I want to work on the larger projects I can think about. So say I load gpt4. How do I get my model a) to be trained and b) to ask me interview questions and adequately respond? In case the explanation is too time-consuming for you, any github/youtube/course etc links that are relevant would suffice. Please assist. submitted by /u/Holiday_Slip1271 [link] [comments]

• [P] A Python Intelligence Config Manager. Superset of hydra+pydantic+lsp
by /u/cssunfu (Machine Learning) on April 23, 2024 at 3:57 pm

I developed a very powerful Python Config Management Tool. It can make your json config as powerful as python code. And very friendly to humans. The most attractive feature is that it will analyze Python code and json config file in real time, provide document display, parameter completion, and goto Python definition from the json config. (Powered by LSP) Similar or better config inheritance, parameter reference and parameter grid search like hydra Data validation similar to pydantic, and the ability to convert dataclass to json-schema This project is still in its early stages, and everyone is welcome to provide some suggestions and ideas. git repo submitted by /u/cssunfu [link] [comments]

• [N] Phi-3-mini released on HuggingFace
by /u/topcodemangler (Machine Learning) on April 23, 2024 at 3:26 pm

https://huggingface.co/microsoft/Phi-3-mini-128k-instruct The numbers in the technical report look really great, I guess need to be verified by 3rd parties. submitted by /u/topcodemangler [link] [comments]

• [D]Drastic Change in the Accuracy score and other measures after hyper parameter tuning.
by /u/Saheenus (Machine Learning) on April 23, 2024 at 1:41 pm

Hey, I am currently doing a malware classification (malware,benign).Used the naive Bayes(Bernoulli) the accuracy was 67 at this point.After the tuning it goes straight up 100. Is this normal or not? I did Outlier removal using the IQR and feature selection using the correlation. submitted by /u/Saheenus [link] [comments]

• [D] How to and Deploy LLaMA 3 Into Production, and Hardware Requirements
by /u/juliensalinas (Machine Learning) on April 23, 2024 at 12:33 pm

Many are trying to install and deploy their own LLaMA 3 model, so here is a tutorial I just made showing how to deploy LLaMA 3 on an AWS EC2 instance: https://nlpcloud.com/how-to-install-and-deploy-llama-3-into-production.html Deploying LLaMA 3 8B is fairly easy but LLaMA 3 70B is another beast. Given the amount of VRAM needed you might want to provision more than one GPU and use a dedicated inference server like vLLM in order to split your model on several GPUs. LLaMA 3 8B requires around 16GB of disk space and 20GB of VRAM (GPU memory) in FP16. As for LLaMA 3 70B, it requires around 140GB of disk space and 160GB of VRAM in FP16. I hope it is useful, and if you have questions please don't hesitate to ask! Julien submitted by /u/juliensalinas [link] [comments]

• [D] Language Model for students
by /u/mbungee (Machine Learning) on April 23, 2024 at 11:31 am

Hello Community, I am preparing a lecture on language models with a lot of hands on work in python. I am trying Llama 3 8b but it seems to run very slow to answer prompts. I have a laptop with a modern I7 and 32GB of RAM. I assume my students have something less powerful and I don’t want them to take hours just for a prompt. So do you know a model that is reasonably fast without giving up too much performance? submitted by /u/mbungee [link] [comments]

• Robotics and AI [D]
by /u/navarrox99 (Machine Learning) on April 23, 2024 at 11:31 am

Hello! I've studied robotics engineering, and my approach to Al has primarily focused on computer vision. I've been deeply interested in this area and, of course, nowadays, I use GPT-4 on a daily basis for both work and personal projects. I'm starting an MSc in Al next year, and in the cover letter for the master's application, I would like to discuss potential research topics that combine robotics and Al. My first choice involves using reinforcement learning for navigation and path planning. I'm also interested in the potential application of vision transformers to visual and semantic SLAM, as well as deep learning-based feature extractors. I'm also impressed by what large companies are achieving with multimodal transformers and humanoid robot like the figure Al, although I understand that these projects might only be feasible for such organizations. I'd love to hear your opinion and insights on the trends in robotics and Al. And receive some guidance from experts on the field. What do you think are the current hot topics, and what will be the key areas of focus in the next 5, 10, and 15 years? Thanks! submitted by /u/navarrox99 [link] [comments]

• [P] I built a website to detect audio deepfakes and spoofs.
by /u/mummni (Machine Learning) on April 23, 2024 at 10:27 am

Hi everybody, I've been working on a project for over two years now: Deepfake-Total.com, a website where you can analyze audio files for traces of text-to-speech or voice conversion, i.e. identify audio deepfakes and spoofs, which I feel is an important topic, especially given the number of important elections coming up. The tool is free-to-use and supports YouTube and twitter URLs, as well as the manual upload of audio files. I wanted to share this and get your feedback: What works for you and what does not, where can I improve? The model should be quite precise for most input, but similar to an anti-virus scanner, there'll always be the occasional outlier. If you find any, feedback is much appreciated, as well as ideas for (scientific) collaboration, etc. submitted by /u/mummni [link] [comments]

• [D] Are there any MoE models other than LLMs?
by /u/lime_52 (Machine Learning) on April 23, 2024 at 9:58 am

Is MoE architecture also applied in other ML areas, let’s say Computer Vision? Why aren’t they popular? Is it because we don’t scale vision transformers as much as LLMs, and MoE is best for scalability? submitted by /u/lime_52 [link] [comments]

• [D] What best practices and workflows those working solo as DS/MLE should keep in mind?
by /u/Melodic_Reality_646 (Machine Learning) on April 23, 2024 at 9:40 am

I'm wondering what technical recruiters or seasoned DS/MLE have to say about people with profiles like mine: good theoretical and decent technical background but working solo for too long. Summary of my career for context: I've been working 8 years now as a DS, the first 3 in medium sized R&D and consulting teams (for a big tech company), then for the past 5 as a solo DS for relatively successful non-ai focused start-ups, mostly developing ML/NLP stuff to address specific issues or improve one specific feature of their product (i.e. never a whole product). In 5 years I designed. developed and deployed, say, 4 models (but experimented with many ofc) - along with a few dashboards and simple streamlit POCs). Recently attending to meetups and seeing how people that make part of actual teams work, discuss and exchange knowledge it suddenly stroke me: I'm missing out, I'm becoming obsolete. I dont feel sharp enough for technical interviews, I'm not sure the way I develop and maintain my projects are following good standards/best practices (heck, i hardly follow a kanban, mostly use my planner to report to my boss on progress). I do some version control and document what I put into prod, but not even that I'm sure I'm doing as it'd be expected within a team. submitted by /u/Melodic_Reality_646 [link] [comments]

• [D] Optimizing performance by reducing redundancy in looping through PyTorch tensors
by /u/zedeleyici3401 (Machine Learning) on April 23, 2024 at 9:18 am

I’m currently working on a project where I need to populate a tensor ws_expanded based on certain conditions using a nested loop structure. However, I’ve noticed that reconstructing this loop each time incurs a significant computational cost. Here’s the relevant portion of the code for context: ws_expanded = torch.empty_like(y_rules, device=y_rules.device, dtype=y_rules.dtype) index = 0 for col, rules in enumerate(rule_paths): for rule in rules: mask = y_rules[:, col] == rule ws_expanded[mask, col] = ws[index][0] index += 1 As you can see, the nested loops iterate over rule_paths and rules to populate ws_expanded based on certain conditions. However, as the size of the tensors increases, reconstructing this loop becomes prohibitively expensive. I’m exploring ways to optimize this process. Specifically, I’m wondering if there’s a way to assign the weights (ws) to ws_expanded permanently using pointers in PyTorch or JAX, thus eliminating the need to reconstruct the loop every time. Could you please advise on the best approach to handle this situation? Any insights or alternative strategies would be greatly appreciated. submitted by /u/zedeleyici3401 [link] [comments]

• [R] Seeking Expert Reviewers for Neural Network-Based Thermal Diffusion Research
by /u/No-Palpitation-7229 (Machine Learning) on April 23, 2024 at 8:44 am

Hello everyone, I'm preparing to submit a research paper and need to identify potential reviewers. My paper introduces a novel approach to solving thermal diffusion problems in steel rods using neural networks. Traditional methods often struggle with complex boundary conditions or nonlinear material properties, but our neural network model, trained on solutions from classical analytical methods, shows promise in predicting temperature distributions accurately with a low error margin. I'm looking for experts with a Ph.D. or M.D. and significant experience in physics, thermal dynamics, or related fields of machine learning. If you have expertise in these areas or know someone who does, I would greatly appreciate your input or referral. What I've done so far: Developed the neural network model and tested it against classical solutions. Drafted the manuscript detailing methodologies, results, and implications. I'm facing a challenge in finding suitable reviewers who have a deep understanding of both thermal physics and machine learning applications. Any guidance or suggestions from this community would be incredibly helpful. Thank you for considering my request! Best regards, Ed submitted by /u/No-Palpitation-7229 [link] [comments]

• [D] Gated Long-Term Memory
by /u/jessielesbian (Machine Learning) on April 23, 2024 at 7:52 am

Today, I am presenting my latest idea: Gated Long-Term Memory GLTM unit Gated Long-Term Memory tries to implement an efficient LSTM alternative. Unlike LSTM, GLTM does all the heavy lifting in parallel, the only operations that are performed sequentially are the multiplication and addition operations. Gated Long-Term Memory uses only linear memory, compared to the quadratic memory of Transformers. submitted by /u/jessielesbian [link] [comments]

• [P] Extensible and Customisable Vertex AI MLOps Platform
by /u/AdComfortable5974 (Machine Learning) on April 23, 2024 at 7:52 am

I've just released an open-source, end-to-end Vertex AI MLOps platform on Google Cloud Platform (GCP). It provides a comprehensive overview of fundamental components and the various operations required to enable such a platform. If you're a team or individual looking to get started with MLOps on GCP, this could be a valuable resource for you. You can read about it on Medium: Extensible and Customisable Vertex AI MLOps Platform submitted by /u/AdComfortable5974 [link] [comments]

• [R] A Survey on Self-Evolution of Large Language Models
by /u/tnlin (Machine Learning) on April 23, 2024 at 7:17 am

Hi everyone, I am the second author (and project leader) and would like to share of our latest work: A Survey on Self-Evolution of Large Language Models. LLMs that use a self-evolution approach have rapidly increased. However, the relationships between these methods remain unclear, lacking systematic organization. https://preview.redd.it/bhfeilfni6wc1.jpg?width=1240&format=pjpg&auto=webp&s=8c268f3033fcd08c55ce860d00ff02c83bcb3884 To bridge the gap, we are pleased to introduce our latest paper, "A Survey on Self-Evolution of Large Language Models", which presents a conceptual framework for the self-evolution of LLMs, enabling models (such as WizardLM, LLAMA, and Phi) to autonomously (1) acquire and (2) refine experiences, (3) update themselves, and (4) evaluate their performance iteratively. https://preview.redd.it/br95klfni6wc1.jpg?width=1500&format=pjpg&auto=webp&s=93f6ae86772e632c168617c4cabd350f892eeedb Our framework explores the potential for LLMs to move from a data flywheel to an intelligent flywheel and hopefully become a new training paradigm that scales LLMs and LLM-base agents towards more autonomous AI systems. For more details, please visit: 📄 Arxiv: https://arxiv.org/abs/2404.14387 🤖 GitHub: https://github.com/AlibabaResearch/DAMO-ConvAI/tree/main/Awesome-Self-Evolution-of-LLM 🐦 Tweet: https://twitter.com/tnlin_tw/status/1782662569481916671 We will keep adding papers and improving the survey and repo. Any suggestions and PRs are welcome! submitted by /u/tnlin [link] [comments]

• [D] Zotero Organization
by /u/Relative_Tip_3647 (Machine Learning) on April 23, 2024 at 7:10 am

People who are using Zotero for organizing and reading research papers, how you guys are using collections, subcollections or tags? Literally, I want to know what are you doing reseach on (vision, language, ...) and what collections, subcollections or tag are you using and how? Recently I have started using Zoteor and I am really confused about it. Looking for inpirations from other people. Thanks in advance. submitted by /u/Relative_Tip_3647 [link] [comments]

• [D] Why ml models on WAWQI ?
by /u/Silver_Bison_4987 (Machine Learning) on April 23, 2024 at 4:53 am

I am doing a project on prediction on the water quality prediction. To train the ml model we need to have x(independent variables) and y(dependent variable) values. I am using the weighted arethamatic water quality index to calculate the value of y from the x using some mathematical equations, Now after calculating the y value I am training the ml models on x and y values. My question is that is ml models worth applying are they doing some add-on to find information? question highlights an important consideration in using ML models for water quality prediction when the Weighted Arithmetic Water Quality Index (WAWQI) is already available I feel that the same thing that is done by the ml model can also be done by calculating the wawqi value for the test data and then tell from the wawqi value that the water is good or not. so why ml models need to be used ? And I have seen some papers doing the same thing but cannot understand why ? helpful inputs are appreciated. submitted by /u/Silver_Bison_4987 [link] [comments]

• Discussion: AI for data science
by /u/SwimmingMeringue9415 (Data Science) on April 23, 2024 at 1:53 am

Do you think that AI can help data science teams beyond just "ask data / text2sql" chatbots? I've been in DS for a while, both as an IC and now as a lead. Despite improvements in analytics tools and workflows, getting to meaningful insights is still a very labor intensive and code heavy process. It especially takes a significant time to perform exploratory/foundational analysis, which can limit the ability to tackle more specialized problems and also increases the risk of overlooking something entirely. I've been building something to address this, here's the elevator pitch: an autonomous AI data scientist that proactively explores data, discovers insights, and presents findings in plain English. This will give data teams an advantage by discovering core insights faster and pinpointing precisely where to initiate more in-depth analysis. I have an MVP that can do what I am promising - users can connect/upload data and the product will iteratively plan, perform analysis, and interpret the results, each time summarizing findings into key themes. Under the hood, I'm using LLMs to orchestrate analysis and interpret results but using robust data science pipelines to perform the actual analysis. Accuracy and reliability is at the core. I'm curious about the community's thoughts on this problem and my approach for a solution. Am I onto something or do I have it wrong? How much time do you/your teams spend on foundational analysis compared to deeper problem-solving or modeling? Is time often a limiting factor to how much you can explore before committing to a certain analysis path? Assuming you could trust its output, do you think "proactive" AI driven insights would be valuable? submitted by /u/SwimmingMeringue9415 [link] [comments]

• [D] Phi-3 to be released soon
by /u/yusuf-bengio (Machine Learning) on April 23, 2024 at 1:13 am

Heard from two independent sources at MSFT (one close to Sebastien Bubeck) about the upcoming Phi-3 models: Three different sized models (up to 14B) Again, mostly synthetic and LLM-augmented training data Apparently some upscaling techniques on the training side No more Apache 2 but more restrictive license (similar to llama3) Mixtral level performance with much fewer parameters I wanted to see if anyone has more insider information about the models. submitted by /u/yusuf-bengio [link] [comments]

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