# 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

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

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.

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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!

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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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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.

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• The 1 Big Thing I've Learned from Data Analysis (Who runs the world?)
by /u/waitingforgoodoh (Data Science) on August 12, 2024 at 12:35 am

• [D] Architecture for Diffusion for Low Data, but PCA suggests also 5%-10% num features of PCA components needed for 80-90% variance explained?
by /u/MysticalDragoneer (Machine Learning) on August 12, 2024 at 12:04 am

I have a dataset, quite few. 2K samples. These are not images, but set data. Each sample is a set of values V with around 50,000 per set/sample. When I perform a PCA, i see that 10% of numV components explain 90% or so of the variance. I tried a simple transformer blocks x 3, and some skip/norms. And trained backward diffusion. The low came low. But when I generated the data, the loss(MSE) was low, but the abs pearson-corr was low so it doesn’t capture the ups and downs as well. Do you guys have any suggestion? For architecture or data representation and so on for a neural network Edit: i might also add, transformers are painful on the time to compute and store the large attention matrix The whole dataset is of shape (2000, 50_000) submitted by /u/MysticalDragoneer [link] [comments]

• [P] Vision Transformer + ChatBot
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Let’s say I want to train a pre-trained Vision Transformer/CLIP model on certain image data and annotations as well as implement it as a chatbot, basically like ChatGPT4.0, how do I do so? I should mention that the annotations for these images would be single/double words but my requirements include that the transformer can somewhat give 4-5 lines of text after scanning an image given it is pre-trained on other image data and has capability to hold a conversation. I have experience in Computer Vision and basic experience with LLMs but this is absolutely another league for me. submitted by /u/DaTrollFace [link] [comments]

• Paid APIs vs local Machine [D]
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I’m considering building a computer with a couple of high-end GPUs for running ML models locally (probably ollama and open WebUI). However, I have run the numbers for the machine build and am now wondering if the money would be better spent on paying for APIs instead. Two RTX 4090 24GB will set me back US$5k alone. I am putting the relevant life-time of these GPUs to 5 years. That's around$85 per month in API tokens. Which would be the better deal? Anyone tackled this ? submitted by /u/mikedensem [link] [comments]

• [D] Need Advice on Fine-Tuning LLMs Locally with Confidential Data and Creating PDF Templates
by /u/thepotentio_reddy09 (Machine Learning) on August 11, 2024 at 6:45 pm

Hi everyone! I'm planning to use the Llama 3.1 70B model on my local machine to fine-tune it with some confidential data from my company. My concern is whether this data could potentially be leaked, even though I'll be running the model locally. Also, could you suggest any good LLMs that might be a better alternative to Llama 3.1 70B? For context, I have a dataset of about 9 PDFs (I know it’s not a lot), which contains a mix of tables and text. When I fine-tune the model, I need it to generate templates in PDF format, focusing on just the tables and headings. Since I’m pretty new to this, I’d really appreciate any advice on how to prepare my dataset and what my next steps should be. Thanks! submitted by /u/thepotentio_reddy09 [link] [comments]

by /u/AutoModerator (Machine Learning) on August 11, 2024 at 3:00 pm

• [Discussion] What dataset should I use for classifying breast cancer based on homologous recombination deficiency?
by /u/icy_end_7 (Machine Learning) on August 11, 2024 at 2:07 pm

https://preview.redd.it/gne7m3lzk1id1.png?width=972&format=png&auto=webp&s=db84e0d9bdbcd2ba756e085c59691bdf5391c937 I've decided to work on a thesis and paper on a very similar topic (using ML for something cancer and genetic data related) and I think this one is good to use as a reference. The author Mia Josephine Jeffris basically chose a transcriptome dataset and used SVC to classifiy cancers into those that had homologous recombination deficiency and those that did not. I plan to use a different model and compare the performance to baseline models (random forest / decision tree/ SVM etc..) and hopefully propose a new model that can classify using fewer features while producing SOTA metrics (AUC and accuracy). My idea is: Find a transcriptome dataset, do some exploration/ preparation/ scaling/ train models and test performance. I also intend to publish this in a relevant journal - so the dataset should be (high dimensional) recent and somewhat large. I'm new to the topic, any pointers? Recent papers on related ideas? I'll be very grateful for the help. submitted by /u/icy_end_7 [link] [comments]

• Bs in data science, masters in computational life sciences. Anyone here have this path? How did life turn out for you?
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How likely can someone switch from life sciences to general data science? As in business domain. submitted by /u/Firm-Message-2971 [link] [comments]

• Auto-Analyst 2.0 — The AI data analytics system. Opensourced with MIT license
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• [Discussion] Resources for onnx model conversion
by /u/JournalistCritical32 (Machine Learning) on August 11, 2024 at 9:07 am

I've been working on an audio-based project for the past six months, primarily using TensorFlow due to the requirement of deploying models with TensorFlow Lite (TFLite). However, I've encountered limitations with TensorFlow in terms of audio-based augmentations like pitch shifting, Room Impulse Response (RIR), and SpecAugment. In contrast, PyTorch offers a richer set of tools for these tasks, making it more suitable for my project needs. Given this, I'm considering switching to PyTorch. However, I still need to convert PyTorch models into TensorFlow models for deployment. During my research, I discovered that ONNX is a popular approach for this conversion. However, it seems that the PyTorch models need to be structured in a specific way to be compatible with TensorFlow after conversion. Does anyone have a guide on how to structure PyTorch models for ONNX conversion, or know of a more flexible conversion technique? TL;DR: I'm working on an audio project using TensorFlow for TFLite deployment but considering switching to PyTorch due to its superior audio augmentation tools. I need to convert PyTorch models to TensorFlow and am looking for guidance on using ONNX for this or any other flexible conversion method. submitted by /u/JournalistCritical32 [link] [comments]

• [P] Vison Language Models from Scratch
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• DS & ML Roadmap: Personal
by /u/PuzzleheadedHouse756 (Data Science) on August 11, 2024 at 7:11 am

I'm listing everything that I've planned to do for DS & ML considering I'm pure noob to programming , stats, probability , linear algebra & calculus. Once i done with all of these then I'll move to machine learning algorithm and deep learning algorithm. Planned to work on everything from open data to research paper on my own, like a private contractor unless full-time jobs get offered. Extra skill: Git , DSA , Tableau and PowerBI, Azure Personal Wishlist: To learn C++ and Rust for fun :)) I'm a data entry employee(Zero Skill job) working in a knowledge outsourcing company based in India. I've planned to work all of these on my own and if you have any suggestions feel free to add in the comment. Programming: 1.Python: Core Python + basics of OOP + Numpy + Pandas + (matplotlib + seaborn) python 1 week 1 project for solid understanding of concepts practice Numpy and Pandas github questions, visulisations tools practice 2. R: learn syntax and implement libraries using dataset 3. SQL: learn all basics to advanced and practice the same from various sources Maths & ML: 1. book reading and practicing accordingly using numpy and pandas libraries 2. a little in-depth study required submitted by /u/PuzzleheadedHouse756 [link] [comments]

• [R] Tree Attention: Topology-aware Decoding for Long-Context Attention on GPU clusters
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A new research paper introduces Tree Attention algorithm for parallelizing attention computation across multiple GPUs, using associative properties of logsumexp and max operations to structure reduction as a tree. Tree attention algorithm, enables cross-device decoding to be performed asymptotically faster (up to 8x faster) than alternative approaches such as Ring Attention, while also requiring significantly less communication volume and incurring 2x less peak memory. submitted by /u/AhmedMostafa16 [link] [comments]

• [D] Noisy generation when traininig Stable Diffusion from scratch
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Hello, I'm training stable diffusion 1.4 from scratch on CIFAR10. I'm using the CompVis implementation with the training script directly taken from: https://github.com/huggingface/diffusers/blob/main/examples/text_to_image/train_text_to_image.py with the necessary modification to take out the VAE from training & inference, and changing sample size 64->32, in/out channel 4->3, and reduction in model size (removed one block of crossattn in both up and downblocks). Everything else are kept the same from the original code. I'm doing fp16 training. However, after sufficient amount of steps (e.g. 170K steps * 8 batchsize) the results are still very noisy and highly saturated. For example the first picture is generation of SD1.4 but with [256, 512, 1024] channels and [down/up2d, crossattn, crossattn], 2 layers per block, trained only on the airplane class. The second is [64, 128, 256] and 1 layer per block, trained on 10 classes. Since the results are so bad, I believe something I'm doing is fundamentally wrong... this is my first time training a SD from scratch so I don't have a very educated guess on the cause... if anyone has any thought on this it would be really appreciated 🙂 Thank you very much!! https://preview.redd.it/y2wbvta1uxhd1.png?width=257&format=png&auto=webp&s=16e4892b46452499363835029944f01c90b9588b https://preview.redd.it/1u5uigp1uxhd1.png?width=1006&format=png&auto=webp&s=570e7e3f0f9ee23aa61f5183e659862173682793 submitted by /u/ImaginaryAd9209 [link] [comments]

• [P] Looking for a gradient descent approach
by /u/IgorTheMad (Machine Learning) on August 10, 2024 at 10:52 pm

I had an idea for an approach to gradient descent that tries to 'jump' directly to a (predicted) location of a nearby minimum. It works by approximating the 2nd-5th order Taylor polynomial around a point, then solving for the minimum (if possible) and setting that point as the new x. Then, the process can be repeated. If the Taylor polynomial at any point is concave, then we can use more standard gradient descent methods. This seems like a rather simple approach, so I doubt it is novel, but I haven't been able to find anything like it online. Does anyone know what this approach is called or if it has been studied? I was inspired by Newton's method for finding roots and a mild disdain for hyperparameter tuning. Here are desmos demos for the quadratic and cubic Taylor approximations: Quadratic Descent: https://www.desmos.com/calculator/i2nsjaxzhy Cubic Descent: https://www.desmos.com/calculator/kgkbcfdn7t submitted by /u/IgorTheMad [link] [comments]

• [R] WildHallucinations: Evaluating Long-form Factuality in LLMs with Real-World Entity Queries
by /u/AhmedMostafa16 (Machine Learning) on August 10, 2024 at 10:12 pm

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• [D] Modeling a dynamic system using LSTM
by /u/WilhelmRedemption (Machine Learning) on August 10, 2024 at 9:15 pm

Dear all, after looking this very well made video about the modeling of a dynamical system using RNN and LSTM I decided to model my real system using the same concept. Basically I want to model the dynamic of my real robot in order to create a "digital twin" of the same. In other words, I want to recreate the same robot in a simulator, with virtual physics properties and move it as it were real. My robot is driven using a joystick which output on every axes a float between -1.0 and 1.0. I collected the data (the real robot hat sensors already working and implemented). For simplification, let's say, that I want to drive the following joint coordinate by moving my joystick axis from left to right (Fig. 1). Fig. 1 I collected one hour long the data, then I trained a LSTM with a hidden size of 32 using the following data: The input is a concatenation of the joystick input and the joint coordinate (the state of the robot) The target is representation by the state of the robot in the next step. I simply copied the columns of the state and shifted it one unit backward. Fig.2 shows probably better then 1000 words. Fig. 2 Then I created sequences of lenght 200 and trained my LSTM. The training converged very quickly and I was quite happy with the results. But somehow the virtual robot reacts strangely in the virtual environment. It jumps from one position to another with incredible speed and then moves very slowly. So it is not reacting as the real robot would move (the real one is more smooth during the movement). Am I missing something important in this kind of problem? What should I still consider, in order to create a good digital twin of the real robot? Note aside: despite the example above, I normalized all the movements into the range [-1, 1] or [0, 1] all the data has been collected using ethernet cable (so no delay due to wireless communication and so on) I used the LSTM classes of PyTorch and not a custom realization The data were collected by generating sinusoids inputs with different frequency and covering all the range of the joint. For the training I shuffled the data: randomly a start index was chosen and a sequence of 200 element was cut and used for training. submitted by /u/WilhelmRedemption [link] [comments]

• [R] Inference AudioCraft MusicGen models using Amazon SageMaker | Amazon Web Service
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