# 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:

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

### AI Dashboard is available on the Web, Apple, Google, and Microsoft, PRO version

and

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

### Invest in your future today by enrolling in this Azure Fundamentals - Pass the Azure Fundamentals Exam with Ease: Master the AZ-900 Certification with the Comprehensive Exam Preparation Guide!

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.

### "Pass the AWS Cloud Practitioner Certification with flying colors: Master the Exam with 300+ Quizzes, Cheat Sheets, Flashcards, and Illustrated Study Guides - 2024 Edition"

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.

# Machine Learning For Dummies App

What are some good datasets for Data Science and Machine Learning?

Machine Learning Engineer Interview Questions and Answers

# 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.

# Pytorch – Computer Application

Best practices for training PyTorch model

### Dive into a comprehensive AWS Cloud Practitioner CLF-C02 Certification guide, masterfully weaving insights from Tutorials Dojo, Adrian Cantrill, Stephane Maarek, and AWS Skills Builder into one unified resource.

What are some ways we can use machine learning and artificial intelligence for algorithmic trading in the stock market?

What are some good datasets for Data Science and Machine Learning?

Top 100 Data Science and Data Analytics and Data Engineering Interview Questions and Answers

Machine Learning Engineer Interview Questions and Answers

• [D] AI/ML in big tech vs biotech
by /u/Pleasant_Wish1799 (Machine Learning) on August 7, 2024 at 5:13 am

I'm curious why a strong ML engineer would leave a big tech firm (like Google, Microsoft or OpenAI) and work for biotech company. What is the appeal to biotech versus all the cutting edge innovation happening in tech companies? submitted by /u/Pleasant_Wish1799 [link] [comments]

• [D] Is "Dopamine Optimizer" the next evolution of AI?
by /u/YanaiEliyahu (Machine Learning) on August 7, 2024 at 4:34 am

Justifications for this claim: Almost everything that deep learning does is "mirroring" human's outputs/skills through data, if an optimizer could optimize based on signals from dopaminergic/serotonergic neurons (e.g. what's good/bad) it could learn anything that a human can do (robotics art driving etc), and might get other benefits humans have. If you had to choose between the 2 top AI models in the world (without knowing which is better), you would go for the one that feels better, so it's better to just automate the development of models search through choosing what feels better and repeat till there are no more choices to make. (cost functions are just proxy to that) Dopaminergic neurons are about a millionth of the human brain, so it's more efficient to learn how they work, rather than learning how the rest of the brain works. submitted by /u/YanaiEliyahu [link] [comments]

• [R] State of the art in Scene Flow Estimation?
by /u/DisciplinedPenguin (Machine Learning) on August 7, 2024 at 4:31 am

What's the state of the art in scene flow estimation? Suggested reads would be very appreciated. submitted by /u/DisciplinedPenguin [link] [comments]

• Unsupervised clustering of transformers-derived embeddings -- what clustering and visualization algorithms to try after k-means + PCA, and is it just HDBSCAN + UMAP these days?
by /u/hesperoyucca (Data Science) on August 6, 2024 at 11:53 pm

Hi all, extremely new to any kind of NLP work and I've presently been assigned to work on a clustering project. With my lack of NLP experience, I started at a fundamental level with TF-IDF and k-means to learn basic terminology for the area. Predictably, I got subpar results from k-means partitioning of a TF-IDF-generated DTM that was very sparse, so I'm now attempting clustering from transformers-derived embeddings of the corpus with pretrained Sentence Transformers models. Following obtaining of my transformers embeddings, I am looking for input regarding clustering and cluster visualization algorithms that are considered good practice beyond the basic k-means clustering with PCA dimensionality reduction. I was thinking of attempting a Gaussian Mixture Model clustering and UMAP (or t-SNE) visualization approach since I'm familiar with expectation-maximization from other work, but I saw a couple of comments from some not robust sources that indicated with little elaboration or justification that GMMs are not a great fit for embeddings and that something like DBSCAN + UMAP (or t-SNE as a fallback) would be better. Is that the case (thinking for GMM perhaps it's the running time/computational cost of the expectation-maximization and issues of GMM with messy data geometry)? And if so, could someone give me an ELI5 for why DBSCAN, spectral clustering, or etc. would be better for embeddings? The comparison table from sklearn's documentation is a start, but I'm looking for just a little bit more detail specific to embeddings. Thank you so much! submitted by /u/hesperoyucca [link] [comments]

• [P] GroundedAI: Open-Source Framework/Models for Efficient LLM Evaluation
by /u/Jl_btdipsbro (Machine Learning) on August 6, 2024 at 11:53 pm

I'm excited to share GroundedAI, an open-source framework I've developed for evaluating large language model application outputs using fine-tuned small language models and specialized adapters. Key features: - Evaluate LLM outputs for toxicity, RAG relevance, and hallucination - Efficient small language models with metric-specific adapters - Local evaluation using less than 5GB VRAM - Easy-to-use Python package - Contends with GPT4 performance at just 3.8B params The framework currently includes three main evaluators: 1. Toxicity Evaluator 2. RAG Relevance Evaluator 3. Hallucination Evaluator Each evaluator uses a base model that merges with a specialized adapter during warmup, allowing for efficient and metric specific evals. Our models are available on Hugging Face: https://huggingface.co/grounded-ai We welcome contributions and feedback from the community. Check out our GitHub repo https://github.com/grounded-ai/grounded_ai for more details and documentation. Let me know if you have any questions or ideas for improvement! submitted by /u/Jl_btdipsbro [link] [comments]

• causal inference folks - which software do you use for work?
by /u/PhotographFormal8593 (Data Science) on August 6, 2024 at 10:50 pm

Hi, I am a doctoral student preparing for DS/economist jobs requiring causal inference skills. I am curious about what software people in the industry mostly use. We used STATA in our causal inference class, and I wonder if the industry prefers Python, R, Matlab, or other languages over STATA. Thank you in advance for your response! submitted by /u/PhotographFormal8593 [link] [comments]

• [D] Why does overparameterization and reparameterization result in a better model?
by /u/Revolutionary-Fig660 (Machine Learning) on August 6, 2024 at 10:43 pm

The backbone for Apple's mobileCLIP network is FastVIT, which uses network reparameterization between train and inference time to produce a smaller network with better performance. I've seen this crop up in several papers recently, but the basic idea is that you overparameterize your model during training and then mathematically reduce it for inference. For example, instead of doing a single conv op you can make two "branches", each of which is an independent conv op and then sum the results. It doubles the parameters of the op during training, but then during inference you "reparameterize" which in this case means adding the weight/biases of the two branches together resulting in a single, mathematically identical conv op (same input, same output, one conv op instead of two summed branches). A similar trick is done by adding skip connections over a few ops during training, then during inference mathematically incorporating the skip into the op weights to produce an identical output without the need to preserve the earlier layer tensors or do the extra addition. The situation seems equivalent to modifying y = a*x + b during training to y = (a1+a2)*x +b1+b2 to get more parameters, then just going back to the base form using a = a1+a2 and b = b1+b2 for inference. I understand mathematically that the operations are equivalent, but I have less intuition regard why overparameterizing for training and then reducing for inference produces a better model. My naive thought is that this would add more memory and compute to the network, reducing training speed, without actually enhancing the capacity of the model, since the overparameterized ops are still mathematically equivalent to a single op, regardless of whether they have actually been reduced. Is there strong theory behind it, or is it an interesting idea someone tried that happened to work? submitted by /u/Revolutionary-Fig660 [link] [comments]

• [R] alphaXiv - a comments section for ArXiv
by /u/Vivid_Perception_143 (Machine Learning) on August 6, 2024 at 7:36 pm

I've been working on an arXiv labs project, alphaXiv.org, which is a comment and discussion section for papers directly built on top of arXiv. I feel that a lot of readers often have the same questions on papers and so I hope having a central forum could be of great to the research community. Last week, we were featured by Stanford's AI Lab. Please check it out and let me know what you think! This project is in active development, so please DM me if you would like to collaborate or have feedback. submitted by /u/Vivid_Perception_143 [link] [comments]

• Tool for manual label collection and rating for LLMs
by /u/levydaniel (Data Science) on August 6, 2024 at 6:09 pm

I want a tool that can make labeling and rating much faster. Something with a nice UI with keyboard shortcuts, that orchestrates a spreadsheet. The desired capabilities - 1) Given an input, you write the output. 2) 1-sided surveys answering. You are shown inputs and outputs of the LLM, and answers a custom survey with a few questions. Maybe rate 1-5, etc. 3) 2-sided surveys answering. You are shown inputs and two different outputs of the LLM, and answers a custom survey with questions and side-by-side rating. Maybe which side is more helpful, etc. It should allow an engineer to rate (for simple rating tasks) ~100 examples per hour. It needs to be an open source (maybe Streamlit), that can run locally/self-hosted on the cloud. Thanks! submitted by /u/levydaniel [link] [comments]

• [Discussion] Beat GPT-4o at Python by searching with 100 dumb LLaMAs
by /u/thundergolfer (Machine Learning) on August 6, 2024 at 5:41 pm

One thing that should be learned from the bitter lesson is the great power of general purpose methods, of methods that continue to scale with increased computation even as the available computation becomes very great. The two methods that seem to scale arbitrarily in this way are search and learning. Richard Sutton, The Bitter Lesson The eponymously distasteful take-away of Richard Sutton’s essay has often been misconstrued: because scale is all you need, they say, smaller models are doomed to irrelevance. The rapid increase in model size above one trillion parameters and the technological limitations of GPU memory together seemed to foreclose on economical frontier intelligence anywhere except at an oligopoly of intelligence-as-a-service providers. Open models and self-serve inference were in retreat. But as the quote above indicates, there are in fact two arrows in the scaling quiver: learning and search. Learning, as we do it now with neural networks, scales with memory at inference time — larger models perform better, ceteris paribus, because they can extract more data from their training set into more circuits and more templates. Search scales smoothly with compute at inference time — compute that can be spent on either producing higher quality candidates or on producing more candidates. In the ideal case, the scaling behavior can be predicted via so-called scaling laws. Recent papers indicate that generative models like LLMs can be scaled up with search. The Large Language Monkeys paper, published on arXiv by Brown, Juravsky, and co-authors last week, includes several results in this vein and indicates that frontier-level intelligence in certain domains can be elicited from smaller models that can run on a single, past-generation GPU. Further, they observed smooth, predictable improvement of performance with scale. Put more simply: where before, it seemed frontier capabilities required one horse-sized duck, it is clear we can now alternatively get them with one hundred duck-sized horses (or, rather, LLaMAs). This weekend, we set out to replicate this finding. Scaling LLaMA 3.1 8B HumanEval on Modal Running all of our experiments, including configuration and testing, cost well under $50. You can find our code here. You can run it yourself without exceeding the$30/month in credits included in Modal’s free tier. Metrics and data: HumanEval and pass@k Continued in original post... submitted by /u/thundergolfer [link] [comments]

• how do you or your organization approach mentorship and continuing education?
by /u/Virtual-Ducks (Data Science) on August 6, 2024 at 4:58 pm

As I try to grow in my own career, and am increasingly in a position to work with more junior team members, I'm curious about how different organizations approach mentorship and continuing education. Questions: Formal Mentorship: Does your organization have a structured mentorship program? If so, how effective is it? Independence vs. Guidance: Are data scientists at your organization expected to work independently, or are there more senior data scientists helping to guide you? Staying Current: How do you stay up-to-date with the latest technologies, tools, and best practices, especially if you don't have technical senior colleagues to learn from, or you need to learn a tool new to your group? Do you feel confident in your abilities to independently learn/apply new skills? If so, what helped you reach that point? In general, I'm curious about what has and has not worked well for you with regards to mentorship. submitted by /u/Virtual-Ducks [link] [comments]

• [P] Grounded SAM 2: Ground and Track Anything
by /u/Technical-Vast1314 (Machine Learning) on August 6, 2024 at 4:55 pm

https://preview.redd.it/13854j03q2hd1.jpg?width=1280&format=pjpg&auto=webp&s=0735848ae40c2591111fa4ed91d2c28ea829c0ac With the release of SAM 2, we have taken the opportunity to update our Grounded SAM algorithm. The biggest improvement in SAM 2 compared to SAM is the expansion of its segmentation capabilities to video, allowing users to interactively segment any object and track it in video. However, the main issue with SAM 2 is that the segmented and tracked objects do not contain semantic information. To address this, we have continued the approach of Grounded SAM by incorporating an open-set detection model, Grounding DINO. This enables us to extend 2D open-set detection to video object segmentation and tracking. We have release our code in https://github.com/IDEA-Research/Grounded-SAM-2 with very easy implementations, which is convenient for users. Project Highlights: In this repo, we've supported the following demo with simple implementations: Ground and Segment Anything with Grounding DINO, Grounding DINO 1.5 & 1.6 and SAM 2 Ground and Track Anything with Grounding DINO, Grounding DINO 1.5 & 1.6 and SAM 2 Detect, Segment and Track Visualization based on the powerful https://github.com/roboflow/supervision library. And we will continue update our code to make it easier for users. submitted by /u/Technical-Vast1314 [link] [comments]

• [P] Identify the faulty components of water-cooled HVAC systems via anomalous sound detection and diagnose ensuing cooling malfunctions via thermal visual anomaly detection. To perform AI-powered features, the device employs Audio MFE and FOMO-AD algorithms in combination with the web application.
by /u/the-amplituhedron (Machine Learning) on August 6, 2024 at 4:44 pm

• "[D]" Per class augmentation for highly imbalanced image data. Good or bad idea?
by /u/Antman-007 (Machine Learning) on August 6, 2024 at 12:17 pm

When solving computer vision problems where the data is highly imbalance, I have come across a number of techniques one could try - ranging from using loss functions tailored for imbalance datasets, class/sample weights, using sampling techniques like SMOTE, weighted random sampler or just regular random sampling as well as using GANs to generate more data of the minority class. I wonder, however if anyone has explored per class augmentations i.e different augmentations applied to the different classes with the minority class being heavily augmented compared to the majority class. I have scoured the internet looking for material indicating why this could be a good or bad idea and its implications to no avail. submitted by /u/Antman-007 [link] [comments]

• [D] RTX 4090 vs L40S for Server
by /u/ouzunkumhavuzu (Machine Learning) on August 6, 2024 at 10:51 am

Hey everyone, our company is in the process of getting a new server for AI tasks, and we're debating between two GPU configurations: 4x RTX 4090 2x L40S We're aware that the 4090s will have higher power consumption and a larger environmental footprint, but we're still considering them due to their cost. our main use cases: Running and fine-tuning small LLMs for classification, embedding, and reranking tasks Potentially running and fine-tuning decoder-only models (llama, gemma, phi...) The GPUs will be in a Kubernetes environment currently we are in a cpu setting in all our machines, so it is quiet a big of a change for us - therefore we want to make sure that we are not missing any important aspects. we'd appreciate insights on the advantages of the L40S in a datacenter setting. What factors might we be overlooking? Are there any datacenter-specific features of the L40S that would be particularly beneficial for our workload? Any guidance or experiences you can share would be greatly appreciated. Thanks!! submitted by /u/ouzunkumhavuzu [link] [comments]

• [Project] - how to showcase reasoning for model missing prediction
by /u/Environmental_Pop686 (Machine Learning) on August 6, 2024 at 10:44 am

Built out a model that predicts demand using marketing spend, number of products available, stock, when we same etc. Shown the model but the finance director wants to know why the model misses its predictions. For example if model predicts £1m revenue and we generate £900k, she wants to know what drove the miss. Any idea on how I showcase this, my initial thought was to output the features we used in prediction against the actual value of the features. So if we said we’d spend £100k on marketing but we spend £90k that could be a driver of the miss? Not a DS, learning on the job. Any thoughts would be appreciated submitted by /u/Environmental_Pop686 [link] [comments]

• AWS to Azure conversion resources?
by /u/Rockingtits (Data Science) on August 6, 2024 at 10:07 am

Hi all, I've just accepted a new MLE role at a company that uses Azure. I'm purely AWS based currently. I have two weeks to do some study, what courses or books would you recommend? Thanks! submitted by /u/Rockingtits [link] [comments]

• [D] Introducing the Open Medical Reasoning Tasks Project : Open Source AI Is the Path Forward
by /u/aadityaura (Machine Learning) on August 6, 2024 at 1:08 am

• What ACTUALLY qualifies you for an applied scientist role?
by /u/AdFew4357 (Data Science) on August 6, 2024 at 12:56 am

I’ve seen a lot of these applied scientist roles on LinkedIn for various companies. Not just faangs. Seems it’s a bit more of a technical DS role. They all say MS or PhD, but part of me wonders if there is a specific thing they are looking for. For any applied scientists here, what actually qualifies you for the roles like that? Is it really just at least a MS? submitted by /u/AdFew4357 [link] [comments]

• [R] State of the art in Scene/3D Model Generation from 2D images
by /u/rosecurry (Machine Learning) on August 5, 2024 at 9:17 pm

What is the current state of the art for scene reconstruction or 3d model generation from video or images? Any papers or architectures I can research? submitted by /u/rosecurry [link] [comments]

taimienphi.vn

### List of Freely available programming books - What is the single most influential book every Programmers should read

#BlackOwned #BlackEntrepreneurs #BlackBuniness #AWSCertified #AWSCloudPractitioner #AWSCertification #AWSCLFC02 #CloudComputing #AWSStudyGuide #AWSTraining #AWSCareer #AWSExamPrep #AWSCommunity #AWSEducation #AWSBasics #AWSCertified #AWSMachineLearning #AWSCertification #AWSSpecialty #MachineLearning #AWSStudyGuide #CloudComputing #DataScience #AWSCertified #AWSSolutionsArchitect #AWSArchitectAssociate #AWSCertification #AWSStudyGuide #CloudComputing #AWSArchitecture #AWSTraining #AWSCareer #AWSExamPrep #AWSCommunity #AWSEducation #AzureFundamentals #AZ900 #MicrosoftAzure #ITCertification #CertificationPrep #StudyMaterials #TechLearning #MicrosoftCertified #AzureCertification #TechBooks