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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:
$$ \hat {\beta }=(X^{\prime }X)^{-1}X^{\prime }Y=\frac {1}{2500}\times 2500\times (-500)=0.20 $$\.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.
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.
Check out this example project on how to find transcripts of audio recordings with positive emotions. A good example of a project demonstrating of extract actionable insights from audio! It takes common voice dataset of audio files from hagging face, applies emotion recognition model and whisper-tiny model for the transcripts. All is organized in a nice looking batch pipeline. An interesting detail - No need to extract archives! This pipeline analyzes audio files directly from tar archives, saving you extra steps. Video: https://www.youtube.com/watch?v=OCm5W0L5BTU Colab notebook: https://colab.research.google.com/github/iterative/datachain-examples/blob/main/audio/hf_common_voice.ipynb Jupyter Notebook: https://github.com/iterative/datachain-examples/blob/main/audio/hf_common_voice.ipynb submitted by /u/dmpetrov [link] [comments]
There was a paper released along with a GitHub repository of an extremely well-made transformer designed for testing out new components. But I can't find it! It's not one of the ones that has existed like HuggingFace ones. Any clue? submitted by /u/Breck_Emert [link] [comments]
Everyone knows the market is bad right now for software engineers. Probably as bad as it's every been. What is the consensus on the job market for data professionals right now? submitted by /u/Will_Tomos_Edwards [link] [comments]
Hello folks, I've been working on an agentic solution where you can have an autonomous agent taking live calls. We're using a pipeline of Speech to Text, LLM for generating responses and then Text to Speech. In this pipeline, Speech to text is causing some issues because it's difficult to determine when exactly a sentence is over since the user can take pauses. Moreover, when multiple inputs go into LLM, multiple responses are generated and they queue up for Text to speech. How would you solve this problem? How would you also handle cases where the user interrupts the agent? submitted by /u/Leo2000Immortal [link] [comments]
We all saw in class the trade off between bias and variance, that we don't want our train loss to keep going down and our test loss go up. But in practice I feel like doing hyperparameter tuning for classic ML models with GridSearchCV / BayesSearchCV is not enough. Even though I do cross validation, the search.best_model obtained at the end is almost always overfitting. How can you actually perform a search that will give you a robust generalized model with higher chances ? submitted by /u/desslyie [link] [comments]
Head to head of meme-interpretability with the same image and text prompt! Anecdotal but interesting responses. Also clear winner! submitted by /u/No_Cartoonist8629 [link] [comments]
In my academic field (social sciences) I deal with the problem of bias in SA models. My previous work showed that deep learning SA systems inherit bias (e.g. nonrepresentative of the population political bias) from annotators: https://arxiv.org/abs/2407.13891 Now I devised a solution that used a technique I call semantic blinding to provide only the bare necessary information for the model to predict emotions in text, leaving no signal for the model to overfit and produce bias from: https://arxiv.org/abs/2411.12493 Interested to hear your thoughts before I publish the SProp Gnn. Do you think it could be useful beyond the academia? submitted by /u/Hub_Pli [link] [comments]
When would the phase 2 decision come out? I know the date is December 9th, but would there be chances for the result to come out earlier than the announced date? or did it open the result at exact time in previous years? (i.e., 2024, 2023, 2022 ....) Kinda make me sick to keep waiting. submitted by /u/No-Style-7975 [link] [comments]
Few months ago, I migrated from TF 2.0 to Jax. I found that jax is significantly faster than Tf. I noticed in the official documentation that it relies on XLA default that uses JIT compilation which makes execution faster. I also noticed that TF graphs also have option to enable JIT compilation with XLA. But still jax dominates TF with XLA. I just want to know why. submitted by /u/Odd-Detective289 [link] [comments]
Multimodal AI is changing the game by combining text, images, and even video into a single, cohesive system. It’s being talked about as a major leap in AI capabilities. What industries do you think will benefit the most from this tech? And are there any challenges you see in integrating these models into everyday use? Would love to hear everyone's thoughts! submitted by /u/Frosty_Programmer672 [link] [comments]
Say you’ve selected the best classifier for a particular problem, using threshold invariant metrics such as AUROC, Brier score, or log loss. It’s now time to choose the classification threshold. This will clearly depend on the use case and the cost/ benefits associated with true positives, false positives, etc. Often I see people advising to choose a threshold by looking at metrics such precision and recall. What I don’t see very often is people explicitly defining relative (or absolute, if possible) costs/ benefits of each cell in the confusion matrix (or more precisely the action that will be taken as a result). For example a true positive is worth $1000, a false positive -$500 and the other cells $0. You then optimise the threshold based on maximum benefit using a cost-threshold curve. The precision and recall can also be reported, but they are secondary to the benefit optimisation and not used directly in the choice. I find this much more intuitive and is my go-to. Does anyone else regularly use this approach? In what situations might this approach not make sense? submitted by /u/hazzaphill [link] [comments]
Hello everyone, I am looking for methods that can automatically categorize and select layers from for transfer learning. If you know any such methods or research please let me know or share. Thanks submitted by /u/reshail_raza [link] [comments]
Imagine a customer support chatbot for an e-commerce platform that retrieves relevant product details from its knowledge base and performs web searches for additional information. Furthermore, it remembers past conversations to deliver a seamless and personalized experience for returning users. Here is how it works: - Store your own data in the knowledge base—in our case, a Website URL. - Convert the data into embeddings and save it in the Qdrant Vector Database. - Use phidata Agentic Workflow to combine Tools, LLM, Memory, and the Knowledge Base. Code Implementation Video: https://www.youtube.com/watch?v=CDC3GOuJyZ0 submitted by /u/External_Ad_11 [link] [comments]
New paper and code for the scale-wise transformer for fast text-to-image generation from our team at Yandex Research Switti outperforms existing T2I AR models and competes with state-of-the-art T2I diffusion models while being faster than distilled diffusion models. Code with checkpoints: https://github.com/yandex-research/switti Generation examples submitted by /u/_puhsu [link] [comments]
Hello everyone, I've been working on a project for some time now and wanted to share a concept I'm exploring. As we know, decision tree-based models typically split the feature space using certain metrics like MSE, entropy, etc. I started thinking about an alternative approach: instead of splitting individual features, what if we could split the entire space directly? However, this seemed quite difficult, as determining boundaries and regions in the space is challenging. Then I had an idea—what if I project the data onto a line within the feature space, and then split that line, like how trees are typically built on individual features? In essence, I’m thinking of projecting points onto a line and then using tree-based methods to split them progressively. Here's a high-level view of the algorithm: Fit a linear regression model to the dataset (normalized values). Project the data onto the line defined by the regression. Apply a decision tree on this projection, effectively splitting one feature (the projection axis). Calculate the residuals and fit another linear model on the residuals, applying boosting in the process. Since the new linear regressions fitted on the residuals will define separate lines, I assume that through boosting, the model will gradually divide the data in the desired manner over time. You can read a more detailed description of the algorithm here: Algorithm PDF. To visualize how the decision boundaries are formed in a 2D dataset: SpaceBoostingRegressor Note: If you want to see a visual example, uploading high-dimensional GIFs can sometimes be an issue. You can check out the example here: Gif on GitHub. Also you can check the code in the repository: Repository This approach is simple because it assumes linearity, and it works in scenarios where there is a high linear correlation between the target and features while also allowing for some non-linear relationships. You can see an example in the repo,example.ipynb file. However, I’m not sure how well it would perform on real-world datasets, as the linear assumption may not always hold. I want to take this algorithm further, but speed is important for scaling. Techniques like PCA don't seem to help because I need the line to reflect the variance in both the target and feature space, rather than just feature variance. I tried using MLPs and extracting the embeddings from a hidden layer before the output layer, which works better since we're evaluating the target in a larger space, but this approach becomes too slow and isn’t feasible in practice. I think this project has great potential, and I’m looking for feedback, ideas, or anyone interested in collaborating. Any comments or suggestions are welcome! submitted by /u/zedeleyici3401 [link] [comments]
Hoping to see if I can find any recommendations or suggestions into deploying R alongside other code (probably JavaScript) for commercial software. Hard to give away specifics as it is an extremely niche industry and I will dox myself immediately, but we need to use a Bayesian package that has primary been developed in R. Issue is, from my perspective, the package is poorly developed. No unit tests. poor/non-existent documentation, plus practically impossible to understand unless you have a PhD in Statistics along with a deep understanding of the niche industry I am in. Also, the values provided have to be "correct"... lawyers await us if not... While I am okay with statistics / maths, I am not at the level of the people that created this package, nor do I know anyone that would be in my immediate circle. The tested JAGS and untested STAN models are freely provided along with their papers. It is either I refactor the R package myself to allow for easier documentation / unit testing / maintainability, or I recreate it in Python (I am more confident with Python), or just utilise the package as is and pray to Thomas Bays for (probable) luck. Any feedback would be appreciated. submitted by /u/Sebyon [link] [comments]
Edit: I have misworded the title as if OpenAI would confirm how O1 was implemented. I have changed the text to reflect what I meant say. I really want to deep dive into the technicals of how the O1 models perform better than previous models. Have researchers come to any definitive agreement as to what OpenAI could have possible done to achieve O1? From reading online I hear about MCTS, COT... etc, but are any of these methods in large agreement by researhers? submitted by /u/Daveboi7 [link] [comments]
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What do you think of the list? What would you add? LeBron James scores 40,000 career points Mondo Duplantis smashes Olympic pole vault records Spain’s historic Euro 2024 victory, featuring - - Lamine Yamal’s stunning debut Rafael Nadal bids farewell to tennis with an emotional retirement Novak Djokovic finally captures Olympic gold in Paris Caitlin Clark and Angel Reese redefine women’s basketball and its impact Record-breaking Super Bowl LVIII captivates millions The AFC Asian Cup and AFCON showcase football’s global influence Simone Biles makes a triumphant Olympic comeback with record-breaking performances Steph Curry delivers an unforgettable Olympic final performance submitted by /u/bakenzo [link] [comments]