# 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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# Machine Learning Breaking News

Transformer – Machine Learning Models

# 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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• [D][R] Synthetic data benchmark
by /u/goncalomribeiro (Machine Learning) on June 20, 2024 at 2:17 am

Came across this benchmark about synthetic data vendors, focused on multi-table (databases) synthesis: https://mltechniques.com/2024/06/15/synthesizing-multi-table-databases-model-evaluation-vendor-comparison/ Does anyone have used one of these vendors already? What are your thoughts? submitted by /u/goncalomribeiro [link] [comments]

• [P] Llama 3 Language Model Implementation from Scratch(one file)
by /u/atronos_kronios (Machine Learning) on June 20, 2024 at 12:26 am

Hey everyone! I'm excited to share my latest project - a from-scratch implementation of the Llama 3 language model! Inspired by the brilliant works of AAAAAAAAAA.org and Andreij Karpathy, I aimed to recreate the Llama3 model in a clear and modular format. 🔗 GitHub Repository: Llama 3 from Scratch This project has been a fantastic learning experience for me, and I hope it helps others in the community who are passionate about AI and machine learning. Check it out, give it a star ⭐, and feel free to contribute or provide feedback! Let's build and learn together submitted by /u/atronos_kronios [link] [comments]

• Text Classification with Multiple Classes (Categories) [P]
by /u/DonThe_Bomb (Machine Learning) on June 19, 2024 at 9:54 pm

Hi all, I'm working on a project to classify textual data in the form of sentences and paragraphs, into a predefined set of categories. I'm working with about 100+ unique categories, which goes far beyond the typical binary classification examples I've encountered online and the multi-classification examples I've seen (3 or 4 categories at most). Specifically, I'm working with help desk tickets and attempting to classify them into 1 of the 100+ categories available At the moment, I'm using SVMs with OvR to carry this out with varying levels of success and I was hoping someone might be able to share alternative methods for carrying out this task? My knowledge of classification algorithms is fairly limited but I have some past experience working with clustering algorithm such as k-nearest neighbours, but I don't think it's practical for text classification in the case but I could be wrong? Thanks submitted by /u/DonThe_Bomb [link] [comments]

• [P] [D] Automatic Image Cropping/Selection/Processing for the Lazy
by /u/PsyBeatz (Machine Learning) on June 19, 2024 at 9:33 pm

Hey guys, So recently I was working on a few LoRA's(Image based models) and I found it very time consuming to install multiple dependencies, half of them clashing with one another, multiple venv handling, etc. For editing captions, that led me to image processing and using birme, which was down at that time, and I needed a solution, making me resort to other websites. And then caption editing took too long to do manually; So, I did what any dev would do: Made my own local script. PS: I do know automatic1111 and kohya_ss gui have support for a few of these functionalities, but not all. PPS: Use any captioning system that you like, I use Automatic1111's batch process captioning. Link to Repo (StableDiffusionHelper) Image Functionalities: Converting all Images to PNG Removal of Same Images Checks Image for Suitability (by checking for image:face ratio, blurriness, sharpness, if there are any faces at all to begin with) Removing Black Bars from images Background removal (rudimentary, using rembg, need to train a model on my own and see how it works) Cropping Image to Face Makes sure the square box is the biggest that can fit on the screen, and then resizes it down to any size you want Caption Functionalities: Easier to handle caption files without manually sifting through Danbooru tag helper Displays most common words used Select any words that you want to delete from the caption files Add your uniqueWord (character name to the start, etc) Removes any extra commas and blank spaces It's all in a single .ipynb file, with its imports given in the repo. Run the .bat file included !! PS: You might have to go in hand-picking-ly remove any images that you don't want, that's something that idts can be optimized for your own taste for making the LoRA's Please let me know any feedback that you have, or any other functionalities you want implemented, Thank you for reading ~ submitted by /u/PsyBeatz [link] [comments]

• [Discussion] Cheaper setup to run the upcoming 400B models?
by /u/t4kuy4x (Machine Learning) on June 19, 2024 at 9:30 pm

I am looking for the “cheapest” option to run one of the upcoming 400B models locally. Any ideas? I guess you would need ideally like 700GB VRAM? That would require like 8 x H100, but that is like crazy expensive. I can buy a house with that 🤣. Some options I was thinking for was: One of the AMD EPYC cpus with 1TB RAM Probably the upcoming Mac Studio M4 Ultra that will likely have 256 unified memory. Not enough but maybe with some quantizated model. ?? Ideally want to keep it under 25k. Any ideas? It seems that’s why AI labs are raising billions, as these GPUs are crazy expensive. submitted by /u/t4kuy4x [link] [comments]

• [P] ThreadQuilt: Search and Summarize Threads
by /u/rodneyslafuente (Machine Learning) on June 19, 2024 at 9:23 pm

• [R] AgileCoder: Dynamic Collaborative Agents for Software Development based on Agile Methodology
by /u/FSoft_AIC (Machine Learning) on June 19, 2024 at 9:16 pm

AgileCoder is new SOTA multi-agent framework for software development that draws inspiration from the widely-used Agile Methodology in professional software engineering. The key innovation lies in its task-oriented approach, where instead of assigning fixed roles to agents, AgileCoder mimics real-world software development by creating a backlog of tasks and dividing the development process into sprints, with the backlog being dynamically updated at each sprint. The evaluation using HumanEval, MBPP, and our manually curated datasets on complex software requirements (named ProjectDev) to produce complete software demonstrates that we outperform ChatDev and MetaGPT. Paper: https://arxiv.org/abs/2406.11912 Code: https://github.com/FSoft-AI4Code/AgileCoder submitted by /u/FSoft_AIC [link] [comments]

• [D] What does it mean to understand? (Chinese room rethinking)
by /u/somethingsomthang (Machine Learning) on June 19, 2024 at 9:01 pm

I was thinking what would happen if a person was taught like an llm. Image learning Chinese only through Chinese text with no translations to English to keep it separated from all previous knowledge. And in that way simulate learning from scratch. If learning was done this way then even if i learn how to respond and write Chinese in a way that seems like i understand, I wouldn't actually have any idea on what is being written. I'd understand the Chinese text, but not the reality it represents. I can't think of any way i could actually understand how anything i could then write in Chinese relates to the real world since a connection was never made to bridge the self contained Chinese knowledge. So i would think that without anything grounding an ai system in reality it's going to be separated from it and in turn be away from what we'd normally call understanding. If the gap here was bridged for example with translations of Chinese and English then in this situation i could then connect it to reality and understand, or if the Chinese was connected to reality more directly with more context than just text. I think understanding Could be described as the ability to predict. So an llm trained on text does have the ability to understand text, But it's understanding doesn't extend to reality, only the ungrounded abstraction of the text. That is to say i think as we are getting system better capable multimodality, text, audio, image, video, 3d or whatever it'll be. That if they are all connected and relating to each other we might have something we can say truly understands like us by being connected to reality. But what do you guys think? submitted by /u/somethingsomthang [link] [comments]

• How important is reputation of your graduate school?
by /u/claudedeyarmond (Data Science) on June 19, 2024 at 8:10 pm

I am debating between the University of Michigan and Georgia Tech for my data science graduate degree. I have only heard great things about Georgia Tech here but I am nervous that it has a lower reputation than the University of Michigan. Is this something I should worry about? Thanks! submitted by /u/claudedeyarmond [link] [comments]

• [N] Ilya Sutskever and friends launch Safe Superintelligence Inc.
by /u/we_are_mammals (Machine Learning) on June 19, 2024 at 7:29 pm

With offices in Palo Alto and Tel Aviv, the company will be concerned with just building ASI. No product cycles. https://ssi.inc submitted by /u/we_are_mammals [link] [comments]

• [P] Understanding Data Annotation in Machine Learning: Essential Steps and Benefits
by /u/Soggy_Example6842 (Machine Learning) on June 19, 2024 at 5:48 pm

Hey Redditors, I'm excited to share some insights on data annotation in the world of Machine Learning (ML) and Artificial Intelligence (AI). Whether you're new to this field or looking to deepen your understanding, here's a concise breakdown of what data annotation is, why it matters, and how it works. What is Data Annotation? Data annotation involves adding labels or tags to data like text, images, and audio. This helps AI systems understand and process information just like humans do. Why is Data Annotation Important? Increases Accuracy: Proper labeling improves the performance of AI/ML models. Accelerates Learning: Helps models quickly grasp and process data. Enhances User Experience: Leads to smarter and more intuitive AI interactions. Boosts Reliability: Ensures consistent and dependable model performance. Benefits for Businesses Better Decision Making: Accurate data enables reliable AI-driven decisions. Efficient Training: Well-labeled data speeds up AI model training. Improved User Interaction: Creates seamless, user-friendly AI experiences. Enhanced Trust: Builds more reliable and trustworthy AI systems. Steps in Data Annotation Collect Data: Gather necessary data (text, images, audio). Preprocess Data: Clean and prepare the data for annotation. Choose Tools: Select the right annotation software. Set Guidelines: Define clear rules for labeling data. Annotate Data: Label the data according to guidelines. Quality Check: Review annotations to ensure accuracy. Export Data: Prepare the annotated data for use in AI models. Challenges in Data Annotation Time-Consuming: Large datasets require significant effort to annotate. Resource Intensive: Requires substantial human and technical resources. Maintaining Consistency: Ensuring uniform quality across large datasets is tough. How to Overcome Challenges Leverage Experts: Consider professional data annotation services. Use Advanced Tools: Employ tools that offer automation and precision. Regular Quality Reviews: Continuously check and validate the annotations. Conclusion Data annotation is the backbone of effective AI/ML applications. It ensures that models are trained correctly, perform reliably, and meet user expectations. submitted by /u/Soggy_Example6842 [link] [comments]

• [D] Monitoring and Debugging RAG Systems in Production
by /u/Jman7762 (Machine Learning) on June 19, 2024 at 5:08 pm

Hi! I’m part of a team from MIT, where we specialize in developing advanced tools for data visualizations of the latent space. We are currently exploring how visualizations can help increase the effectiveness of RAG monitoring systems and would love to gather insights from how people manage RAGs currently. We know there are existing monitoring tools like Ragas, Arize(Phoenix), LangSmith. We are curious on how Frequency you are looking at monitoring data What does the end-user application your RAG support look like? We believe that a visualization tool could greatly enhance the ability to monitor and debug RAG systems in real-time by: Providing intuitive, graphical representations of system performance and behavior. Highlighting potential issues and bottlenecks at a glance. If you’re willing to share more detailed insights through an interview, please let us know! Happy to get connected and learn more! submitted by /u/Jman7762 [link] [comments]

• [P] [D] Updated On: Hi I'm a senior machine learning engineer, looking for for buddies to build cool stuff with!
by /u/Rude-Eye3588 (Machine Learning) on June 19, 2024 at 3:59 pm

Old Post: https://www.reddit.com/r/MachineLearning/comments/1dj8pg6/p_d_hi_im_a_senior_machine_learning_engineer/ Wow, I wasn't expecting this post to gain so much attention! I've created a Google form for those who are serious about working on projects, Kaggle competitions, or Leetcode challenges. Please take a moment to fill it out. Form: https://forms.gle/k3jzCfNJy3rgz4ec6 Here's how it will work: I will create groups based on your goals and expertise. Each group will have a team leader to assist with progress, alongside my support. It will take some time to organize everyone into teams, so please be patient. I'll reach out to you soon. Thank you! submitted by /u/Rude-Eye3588 [link] [comments]

• [D] Do SIREN networks not generalize in the regression setting, or are there some tricks?
by /u/internet_ham (Machine Learning) on June 19, 2024 at 3:00 pm

I have a tricky regression problem that is high-dimensional and high-frequency. The MSE for a typical MLP (3-4 layers, swish activations) was around 0.1 when I was looking for MSE. I thought I would try SIREN since the MLP seems to struggle with the high frequency components, and in this regard it is amazing and I can get it down to and MSE of 1e-4. The catch is it doesn't seem to generalise in any way. The validation MSE just sits at the same value during training, which makes sense if the model is doing random Fourier feature like model fits but is not what I need. Do you know of any tricks to get this sort of model to generalise better? submitted by /u/internet_ham [link] [comments]

• [P] [D] Video lecture summarization with text+screenshots
by /u/chilled_87 (Machine Learning) on June 19, 2024 at 1:51 pm

I created this app vi-su.app that does just that. I post it here since I am in the ML field, and actually designed this app to help me to preview/remember video tutorials/courses on ML (as there are too many I wish to watch). It relies on a vision-language model to do the job, so inaccuracies can happen, but it usually does a good job. Latest example was yesterday with the 7th lecture of the intro to deep learning from MIT - and the summary there https://vi-su.app/P7Hkh2zOGQ0/summary.html gives in my opinion a good account of the lecture. See other examples in the search tab. Let me know if you find this useful or have suggestions. Depending on interest, I could also open-source it . submitted by /u/chilled_87 [link] [comments]

• Movies where the lead character is a data scientist
by /u/Emotional-Rhubarb725 (Data Science) on June 19, 2024 at 1:35 pm

I feel we aren't well represented in the film industry and I was looking for movies where the lead character is a data scientist or something similar submitted by /u/Emotional-Rhubarb725 [link] [comments]

• good podcasts for data science
by /u/Emotional-Rhubarb725 (Data Science) on June 19, 2024 at 1:34 pm

can you recommend good podcasts for data science ? submitted by /u/Emotional-Rhubarb725 [link] [comments]

• [P] [D] Looking for ways to optimize training of language model on Apple M1
by /u/PickleFart56 (Machine Learning) on June 19, 2024 at 1:21 pm

I have been training tiny language model on my MacBook (M1 Pro), currently it takes about 3-4 hr to train gpt like model (5M params) for about 10k steps with context length of 256 and batch size of 128. Single step is taking about 0.95s or about 35 tokens/s. Also estimated flop utilization and it's coming around 25% assuming M1 Pro has a limit of 5.12TFLOPS. I already tried different batch sizes with gradient accumulation, didn't help much. Is there a way I can further reduce the training time as flop utilization is about 25% only. submitted by /u/PickleFart56 [link] [comments]

• What is the exact purpose of input modulation gate in LSTMs? [R]
by /u/RoomProfessional7018 (Machine Learning) on June 19, 2024 at 1:03 pm

Basically, I was learning about LSTMs where I found LSTMs are made up of three gates: The forget gate, input gate and output gate. However, I came across some sources that state there is a fourth gate called hte input modulation gate. Yet, I can't find much information about this gate. Some sources say it's usually omitted when defining the input gates. Other sources say it's part of the input gate as a sort of sub-system. What exactly does the input modulation gate do in LSTMs? submitted by /u/RoomProfessional7018 [link] [comments]

• [D] ML Journal with fast review time
by /u/MadScientist-1214 (Machine Learning) on June 19, 2024 at 11:47 am

Does anybody know a journal with a fast review time? Maybe max. 6 months. However, the journal should not be too competitive. It's about a computer vision paper that was rejected for CVPR. I already know TMLR. submitted by /u/MadScientist-1214 [link] [comments]

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