**What are the top 3 methods used to find Autoregressive Parameters in Data Science?**

In order to find autoregressive parameters, you will first need to understand what autoregression is. **Autoregression is a statistical method used to create a model that describes data as a function of linear regression of lagged values of the dependent variable**. In other words, it is a model that uses past values of a dependent variable in order to predict future values of the same dependent variable.

In time series analysis,** autoregression is the use of previous values in a time series to predict future values.** In other words, it is a form of regression where the dependent variable is forecasted using a linear combination of past values of the independent variable. The parameter values for the autoregression model are estimated using the method of least squares.

The autoregressive parameters are the coefficients in the autoregressive model. These coefficients can be estimated in a number of ways, including ordinary least squares (OLS), maximum likelihood (ML), or least squares with L1 regularization (LASSO). Once estimated, the autoregressive parameters can be used to predict future values of the dependent variable.

To find the autoregressive parameters, you need to use a method known as** least squares regression**. This method finds the parameters that minimize the sum of the squared residuals. The residual is simply the difference between the predicted value and the actual value. So, in essence, you are finding the parameters that best fit the data.

**How to Estimate Autoregressive Parameters?**

There are three main ways to estimate autoregressive parameters: ordinary least squares (OLS), maximum likelihood (ML), or least squares with L1 regularization (LASSO).

**Ordinary Least Squares**: Ordinary least squares is the simplest and most common method for estimating autoregressive parameters. This method estimates the parameters by minimizing the sum of squared errors between actual and predicted values.

**Maximum Likelihood**: Maximum likelihood is another common method for estimating autoregressive parameters. This method estimates the parameters by maximizing the likelihood function. The likelihood function is a mathematical function that quantifies the probability of observing a given set of data given certain parameter values.

**Least Squares with L1 Regularization**: Least squares with L1 regularization is another method for estimating autoregressive parameters. This method estimates the parameters by minimizing the sum of squared errors between actual and predicted values while also penalizing models with many parameters. L1 regularization penalizes models by adding an extra term to the error function that is proportional to the sum of absolute values of the estimator coefficients.

**Finding Autoregressive Parameters:** The Math Behind It

To find the autoregressive parameters using least squares regression, you first need to set up your data in a certain way. You need to have your dependent variable in one column and your independent variables in other columns. For example, let’s say you want to use three years of data to predict next year’s sales (the dependent variable). Your data would look something like this:

| Year | Sales |

|——|——-|

| 2016 | 100 |

| 2017 | 150 |

| 2018 | 200 |

Next, you need to calculate the means for each column. For our sales example, that would look like this:

$$ \bar{Y} = \frac{100+150+200}{3} = 150$$

Now we can calculate each element in what’s called the variance-covariance matrix:

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

and

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

For our sales example, that calculation would look like this:

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

and

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

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.

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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] Spatial clustering invariant to scale & orientation?by /u/Head-Hole (Machine Learning) on March 4, 2024 at 1:44 am
I'm working on an unsupervised clustering project using spatial map data (raster coverage, not points). My baseline is using zonal statistics aggregated in defined areas, then throwing these in K-means and DBSCAN. They work ok, but I'd really like to find a way to capture spatial relationships at different scales, but are invariant to orientation. In other words, two zones have spatial relationships that mirror each other geographically, but should be grouped together. I was thinking of using a convolutional autoencoder next trained on the different zones, and then clustering their latent representations. Any thoughts or suggestions? submitted by /u/Head-Hole [link] [comments]

- [D] Hypothesis-Driven Learning | Biomimicryby /u/Playful-Struggle4746 (Machine Learning) on March 4, 2024 at 1:14 am
Throughout the day when I observe things (like a social interaction) I formulate hypotheses in my head about why that thing happened or what this means for my life strategy. When I get such a hypothesis I got it down in my notes app or something like that. Of course, this happens in addition to the intuitive learning and automatic, subconscious hypothesizing that we all do. Is there an ML algorithm that behaves like this? submitted by /u/Playful-Struggle4746 [link] [comments]

- [D] does anyone here know intermediate result?by /u/Kindly-Song5246 (Machine Learning) on March 4, 2024 at 12:50 am
My external is asking me to put intermediate result . I am trying to do fake news classification using tf-idf and glove. What would be intermediate result of text classification? I didn't understand. submitted by /u/Kindly-Song5246 [link] [comments]

- [P] Computer Vision Challenge: Validate Detections in Rows and Columnsby /u/zerojames_ (Machine Learning) on March 3, 2024 at 11:28 pm
submitted by /u/zerojames_ [link] [comments]

- [D] How useful is DCN compared to good old MLP?by /u/Crazy_Suspect_9512 (Machine Learning) on March 3, 2024 at 11:15 pm
In industrial large scale search/recommendation context, DCN seems to be still a popular kid on the street, compared to more straightforward MLP. The idea feels more or less like ResNet, where the original raw input keeps showing up at every layer. But is the element-wise product of layer output of raw input really adding any value here? If so why is it not adopted by the transformer architecture? submitted by /u/Crazy_Suspect_9512 [link] [comments]

- [P] Serious differences between cross-validation accuracy and test accuracy. Imbalanced data (combination of over and undersampling) + PCA performedby /u/Abject_Pomegranate39 (Machine Learning) on March 3, 2024 at 8:40 pm
So I am training a SVM model on a dataset with more than 500.000 observations that is also seriously imbalanced. So after splitting my data into training and test data set, I undersampled and oversampled the majority and minority class respectively. Because the data also had more than 50 features I performed a PCA on the training set and decided to keep the first 10 components. Then, I did a cross validation as you can see on the picture below. The Gaussian kernel performed the best. Then I again trained a model on my training set with the Gaussian kernel and tried to predict the test set (which I also performed PCA on). But now the accuracy dropped to 6% (?!). I know that there can be some overfitting but the difference here is so big that I am wondering if there is a problem in the setup of my code? https://preview.redd.it/r7mxa8byi6mc1.png?width=818&format=png&auto=webp&s=afc51f0352312c57febb12220e2804fcb591369d https://preview.redd.it/0iqa0xy2j6mc1.png?width=1093&format=png&auto=webp&s=ec5609ad081f0fc0766317b622b86118302435c7 submitted by /u/Abject_Pomegranate39 [link] [comments]

- [D] Neural Attention from the most fundamental first principlesby /u/AvvYaa (Machine Learning) on March 3, 2024 at 7:59 pm
Sharing a video from my YT that explains the origin of the Attention architecture before it became so ubiquitous in NLP and Transformers. Builds off first principles and goes all the way to some of more advanced (and currently relevant) concepts. Link here for those who are looking for something like this. submitted by /u/AvvYaa [link] [comments]

- [R] Humanoid Robot Dancing, High Five, Waving, Huggingby /u/XiaolongWang (Machine Learning) on March 3, 2024 at 7:37 pm
submitted by /u/XiaolongWang [link] [comments]

- [N] LLM models up to 7 times acceleration.by /u/idlemonk111 (Machine Learning) on March 3, 2024 at 5:08 pm
submitted by /u/idlemonk111 [link] [comments]

- [D] Types of RAG Implementations and Their Benefits?by /u/Lyriciseofficial (Machine Learning) on March 3, 2024 at 4:22 pm
Hey everyone, I recently delved into the world of RAG (Retrieval-Augmented Generation) and discovered its immense potential for enhancing chatbots and other generative models. However, I'm curious about the various types of implementations of this approach and how we can determine which is the most effective. Surprisingly, there's limited information available on different approaches online. Can anyone shed some light on this and share insights on identifying the best implementation? Your expertise would be greatly appreciated! Thanks in advance! submitted by /u/Lyriciseofficial [link] [comments]

- [P] LaVague: Open-source Text2Action AI pipeline to turn natural language into Selenium codeby /u/Separate-Still3770 (Machine Learning) on March 3, 2024 at 3:38 pm
🌊 Released #LaVague, fullly open-source AI pipeline to turn natural language into browser actions! In less than 150 lines of code (RAG with local embedding + Mixtral on Hugging Face API), it generates Selenium code from user query. In this GIF you can see it follow user instructions to command a browser to browse HF website! https://i.redd.it/vf91c2if25mc1.gif Try it on Colab: https://colab.research.google.com/github/dhuynh95/LaVague/blob/main/LaVague.ipynb GitHub: https://github.com/dhuynh95/LaVague Pretty exciting how it becomes possible to create an AI assistant that could perform actions for us, such as logging on gov accounts, fill forms, or pull personal information! It was quite fun to hack in the weekend using open-source tools, from Hugging Face local embedding with transformers + HF Pro API, to RAG with Llama Index, through Mistral Mixtral model! Some challenges: to make it run on Colab for the GPU Poors, I had to resort to HF Inference API with Mixtral as it was the only model good enough (gemma-7b did not make it and refused to produce code). Because I used an off-the-shelf model, I had to improve performance with few-shot learning and Chain Of Thought, the model managed to generate appropriate code! Potential next steps: fine-tune a 2b or 7b model to run fully locally so that everyone can benefit from a transparent and customizable AI agent to take actions for us It might be hard for me to fully grow this project, so I am open to contribution 🙂 submitted by /u/Separate-Still3770 [link] [comments]

- Best approach to predicting one KPI based on the performance of another?by /u/yrmidon (Data Science) on March 3, 2024 at 2:59 pm
Basically I’d like to be able to determine how one KPI should perform based on the performance of anotha related KPI. For example let’s say I have three KPIs: avg daily user count, avg time on platform, and avg daily clicks count. If avg daily user count for the month is 1,000 users then avg daily time on platform should be x and avg daily clicks should be y. If avg daily time on platform is 10 minutes then avg daily user count should be x and avg daily clicks should be y. Is there a best practice way to do this? Some form of correlation matrix or multi v regression? Thanks in advance for any tips or insight EDIT: Adding more info after responding to a comment. This exercise is helpful for triage. Expanding my example, let’s say I have 35 total KPIs (some much more critical than others - but 35 continuous variable metrics that we track in one form or another) all around a user platform and some KPIs are upstream/downstream chronologically of other KPIs e.g. daily logins is upstream of daily active users. Also, of course we could argue that 35 KPIs is too many, but that’s what my team works with so it’s out of my hands. Let’s say one morning we notice our avg daily clicks KPI is much lower than expected. Our first step is usually to check other highly correlated metrics to see how those have behaved during the same period. What I want to do is quantify and rank those correlations so we have a discreet list to check. If that makes sense. submitted by /u/yrmidon [link] [comments]

- [D]Agents+ LLM in productionby /u/Electrical_Study_617 (Machine Learning) on March 3, 2024 at 2:57 pm
Hi everyone, I've noticed that Agents+LLM is gaining popularity lately. Can anyone share which Agentic frameworks are being used in production workloads? Are any of you using a combination of RAG Frameworks with Agents? Also, what are some typical production issues you've encountered while working with Agent Frameworks? Do share your thoughts and insights submitted by /u/Electrical_Study_617 [link] [comments]

- [D] Current models for medical image generationby /u/idontcareaboutthenam (Machine Learning) on March 3, 2024 at 2:43 pm
I'm looking for some up-to-date architectures or models for medical image generation. Since it's medical images data are few (so probably not diffusion) and images should be sharp to make the presence of pathologies clear (so probably not vanilla VAEs). There's many different flavors of GANs and I've found some that work for my case but I'm wondering if I've missed anything. Some sort of latent encoding would be useful too for downstream tasks, so an encoder-decoder architecture would be ideal but I've had some success with GAN inversion. submitted by /u/idontcareaboutthenam [link] [comments]

- [D] How to effectively use date attribute while implementing fake news classification?by /u/Kindly-Song5246 (Machine Learning) on March 3, 2024 at 2:06 pm
I am researching fake news classification. I want to use all four attributes: title, text, subject, and date as all attributes in the dataset give meaningful info. However, I am slightly confused about how to effectively use the date attribute as it is in a number format like 2017-11-30. I am trying to concatenate all four attributes before feeding them to the LSTM Model. submitted by /u/Kindly-Song5246 [link] [comments]

- [P] Research Papers in February 2024 — A Potential LoRA Successor, Small Finetuned LLMs Vs Generalist LLMs, and Transparent LLM Researchby /u/seraschka (Machine Learning) on March 3, 2024 at 2:02 pm
submitted by /u/seraschka [link] [comments]

- [D] How to detect or speculate the "reward-hacking" phenomenon?by /u/zetiansss (Machine Learning) on March 3, 2024 at 1:57 pm
I'm reading the DeepMind paper "WARM: On the Benefits of Weight Averaged Reward Models". The paper is talking about the reward-hacking phenomenon. In the paper, the authors use the KL-reward curve to detect reward-hacking phenomenon, saying that the reward starts to decrease and thus reward hacking happens. However, previous papers like https://arxiv.org/pdf/2312.09244.pdf or https://arxiv.org/pdf/2312.09244.pdf often use two reward models to detect reward hacking: the proxy reward and the true reward. The policy model is updated under the proxy reward, so when the KL increases, the proxy reward will increase too. The reward hacking phenomenon happens when the true reward starts to decrease, which is treated as the detector. So since WARM only shows the reward starts with an increase and ends with a decrease (which is the proxy reward and thus not enough), I don't think it can show the reward hacking phenomenon happening. Hoping for your comments. https://preview.redd.it/4ajcprcjk4mc1.jpg?width=824&format=pjpg&auto=webp&s=756876807aa48d9fffe284f1f51f6ebfd6d877e6 https://preview.redd.it/k00e2rcjk4mc1.jpg?width=793&format=pjpg&auto=webp&s=916ab66eafbe3db0edb705797024c29de3eb798f submitted by /u/zetiansss [link] [comments]

- [P] Need help fine-tuning a LLM to act as an AI teacher (similar to harvard's CS50 chatbot)by /u/Shaheer_Humayun (Machine Learning) on March 3, 2024 at 1:17 pm
I’m working on a project to create a model that can act as an AI teacher for students in an intro to programming class. The model should not write the code for them, but guide them and clear their confusions. I want to fine-tune a large language model for this purpose, but I’m not sure how to go about it. I have some questions that I hope you can help me with: Which LLM should I use? . How should I prepare my dataset? submitted by /u/Shaheer_Humayun [link] [comments]

- [Discussion] [Research] Questions Machine Learningby /u/Stefano939393 (Machine Learning) on March 3, 2024 at 12:36 pm
Dear ML Community, I got some questions since some time and I've been doing my research but I cant find the answers so I've arrived to the point where I need to ask these to see if someone has something to say on it. If you have something to say just to one of these questions, please answer. All these questions are done in the context of designing and building Large Models in a subject different than NLP, specifically animation generation: Are there ways to roughly estimate the relation between dataset_size, model_size and accuracy? Ways different than empiric methods? (since we are talking about large model, I think is too expensive to iterate over many sizes to understand these relation empirically) When building a Large Model. What you increase specifically, number of layers, hidden dim or num of heads? I am particularly curios on the hidden_dim size. I don't think you add value by increasing that dimension as you want. To keep it simply, let's think my token dim size is 1024. I think if you increase the hidden dim size above that number you would be wasting space to storage information. There should be a transformation from the token to the encoded vector that maintain or decrease dimension (to extract valuable features). Therefore increase dimension from the token dimension is a waste of parameters. Thank you for given your thoughts submitted by /u/Stefano939393 [link] [comments]

- [D] Simulated Annealing and Gradient Descentby /u/Due-Outside-8526 (Machine Learning) on March 3, 2024 at 12:23 pm
First of all I would like to apologise if my question is irrelevant. I am a beginner in the field of data science and I’ve been using gradient descent to find the minimum of a function. ( I’m using python) Obviously, I came across the local minimum problem and tried to find ways to avoid it and found simulated annealing. Is there a way to combine both to get to the global minimum? Thanks in advance submitted by /u/Due-Outside-8526 [link] [comments]