**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.

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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- [R] Drive Like a Human: Rethinking Autonomous Driving with Large Language Modelsby /u/MysteryInc152 (Machine Learning) on September 29, 2023 at 10:49 pm
Paper - https://arxiv.org/abs/2307.07162 submitted by /u/MysteryInc152 [link] [comments]

- [Research] - Resource to query ML and LLM based researchby /u/_llama2 (Machine Learning) on September 29, 2023 at 10:00 pm
Made a repo for you all to try using a collaborative AI tool which includes 100+ papers on LLM-Based-Agents. You can try out the repo here: https://www.collama.ai/varun/llm-based-agents submitted by /u/_llama2 [link] [comments]

- [D] Choosing the best learning model for a start up app?by /u/Willy988 (Machine Learning) on September 29, 2023 at 9:30 pm
Straight off the bat: I am not very familiar but was tasked to find a suggest a reasonable model for our need. Here is a bit what I read: https://www.obviously.ai/post/how-to-choose-the-right-ai-model-for-your-application https://www.addevice.io/blog/ai-framework-for-app-development The app that I am working on is an education app, and the purpose of the AI would be to (at least in terms of priority) generate a post subject line / topic to discuss. The company is super small, so money is important. JS is being used mainly at the moment. What would be a good choice for a small start up to generate topics for an education app used by schools? At least any ideas or things to consider would be wonderful to get my rabbit hole dive started! Thanks. submitted by /u/Willy988 [link] [comments]

- [R] Gsgen: Text-to-3D using Gaussian Splattingby /u/Sirisian (Machine Learning) on September 29, 2023 at 8:38 pm
Project Page Paper Code In this paper, we present Gaussian Splatting based text-to-3D generation (GSGEN), a novel approach for generating high-quality 3D objects. Previous methods suffer from inaccurate geometry and limited fidelity due to the absence of 3D prior and proper representation. We leverage 3D Gaussian Splatting, a recent state-of-the-art representation, to address existing shortcomings by exploiting the explicit nature that enables the incorporation of 3D prior. Specifically, our method adopts a progressive optimization strategy, which includes a geometry optimization stage and an appearance refinement stage. In geometry optimization, a coarse representation is established under a 3D geometry prior along with the ordinary 2D SDS loss, ensuring a sensible and 3D-consistent rough shape. Subsequently, the obtained Gaussians undergo an iterative refinement to enrich details. In this stage, we increase the number of Gaussians by compactness-based densification to enhance continuity and improve fidelity. With these designs, our approach can generate 3D content with delicate details and more accurate geometry. Extensive evaluations demonstrate the effectiveness of our method, especially for capturing high-frequency components. submitted by /u/Sirisian [link] [comments]

- [D] Does anyone else feel like MOJO isn't getting the attention it deserves?by /u/hai_cben (Machine Learning) on September 29, 2023 at 8:36 pm
https://docs.modular.com/mojo/ submitted by /u/hai_cben [link] [comments]

- [P] Carton – Run any ML model from any programming languageby /u/vpanyam (Machine Learning) on September 29, 2023 at 7:28 pm
Hi! I just open-sourced a project that I've been working on for a while and wanted to see what you think! The goal of Carton (https://carton.run) is to let you use a single interface to run any machine learning model from any programming language. It’s currently difficult to integrate models that use different technologies (e.g. TensorRT, Ludwig, TorchScript, JAX, GGML, etc) into your application, especially if you’re not using Python. Even if you learn the details of integrating each of these frameworks, running multiple frameworks in one process can cause hard-to-debug crashes. Ideally, the ML framework a model was developed in should just be an implementation detail. Carton lets you decouple your application from specific ML frameworks so you can focus on the problem you actually want to solve. At a high level, the way Carton works is by running models in their own processes and using an IPC system to communicate back and forth with low overhead. Carton is primarily implemented in Rust, with bindings to other languages. There are lots more details linked in the architecture doc below. Importantly, Carton uses your model’s original underlying framework (e.g. PyTorch) under the hood to actually execute the model. This is meaningful because it makes Carton composable with other technologies. For example, it’s easy to use custom ops, TensorRT, etc without changes. This lets you keep up with cutting-edge advances, but decouples them from your application. I’ve been working on Carton for almost a year now and I open sourced it on Wednesday! Some useful links: Website, docs, quickstart - https://carton.run Explore existing models - https://carton.pub Repo - https://github.com/VivekPanyam/carton Architecture - https://github.com/VivekPanyam/carton/blob/main/ARCHITECTURE.md Please let me know what you think! submitted by /u/vpanyam [link] [comments]

- Does my personal business experience matter?by /u/Basic_Set3926 (Data Science) on September 29, 2023 at 6:40 pm
I’m close to taking the Google data analytic certificate test and in this time I’m trying to setup my resume but don’t know if I should simply show my certificates, and education along with my restaurant experience, (what I’ve done to live this far) or if i should also include my personal business experience, such as writing a business book, acquiring investors, launching a business, working with people on marketing projects etc. or if i shouldn’t put anything and just showcase my education? What matters in a resume with only education in the field? submitted by /u/Basic_Set3926 [link] [comments]

- When a ML algorithm is training, what is actually happening behind the scenes? How does it learn?by /u/alpha-gamma-x (Data Science) on September 29, 2023 at 6:34 pm
Basically the question. When we run say logistic regression or an SVM on Python, what is happening step by step with all the train data? I know the answer may vary based on the algorithm, so you may pick any algorithm to explain in detail the behind-the-scenes. Wanted to post at r/explainlikeimfive but wasn’t sure if any ML people may be in that crowd, but please ELI5. submitted by /u/alpha-gamma-x [link] [comments]

- [P] Location Computationby /u/Longjumping-Song4958 (Machine Learning) on September 29, 2023 at 6:31 pm
Hi Everyone, I’m doing a project where I’m crowdsourcing a lot of location data for a set of location labels and then trying to cluster it for each and using the centroid of the cluster as the most accurate location for that location label. The data keeps coming in everyday. I’m not sure when to stop computation. Initially I thought I’ll check the delta between each days centroid computed and if the delta falls under a threshold then stop computing. But now I’m thinking if my daily data collected gets marked as outliers, subsequent days centroids won’t have much of a delta and it will pass my convergence condition. Any suggestions? submitted by /u/Longjumping-Song4958 [link] [comments]

- Anaconda report on the state of Data Science for 2023by /u/Dry_Cattle9399 (Data Science) on September 29, 2023 at 6:22 pm
Hi have anyone checked the latest report from Anaconda: https://www.anaconda.com/state-of-data-science-report-2023? It seems like data prep, data cleaning and data visualization are tasks are the top 3 of the most time consuming? What do you think? submitted by /u/Dry_Cattle9399 [link] [comments]

- US universities to pursue masters in Data Scienceby /u/Professional-Ant5049 (Data Science) on September 29, 2023 at 6:14 pm
Can anyone recommend me reputed US based universities to pursue my masters in Data Science from? Feel free share your thoughts and experiences of the program and university I have a BSC in data science with a concentration in Business Analytics and a minor in mathematics( focusing on statistic courses) from University Of Illinois At Chicago. Additionally, could you include the advantages I would be having of taking that particular program at that particular university for my future , the duration of their programs, proximity to finding internship and career opportunities, Faculty reputation of the university as well as the program , for a perspective student? submitted by /u/Professional-Ant5049 [link] [comments]

- Bachelor Degree in D. Scienceby /u/Late-Tangerine7361 (Data Science) on September 29, 2023 at 5:53 pm
Hello all. I will begin my journey in Data Science. Is there any advices and tips you redditors would like to share? submitted by /u/Late-Tangerine7361 [link] [comments]

- Should I rush to apply for a MSDS in 2024, or increase my knowledge and flair in data science before applying for MSDSby /u/Chattyyyee (Data Science) on September 29, 2023 at 5:48 pm
My profile: I am currently 23 years old with a Bachelor's in Data science, currently working with a FAANG company for 1.5 years. However, the position I work for is a business analytics one, and wanting to make a switch to a pure modelling/ML/AI, as creating decks is not for me, but good with analytics. My Dilemma: First side of the coin: Should I rush for a master's abroad in the States ( includes rushing GRE prep, application requirements etc ) which makes for a crazy 3 months for Fall 2024, as this saves me a year in life, and in sync with not losing out on much. Second side: Take a year and a half to prepare, get in touch with lost data science skills, and see if it still interests me, and if I can be good at it. I also have not networked enough within my company and want more time to create connections or should I take the year to prepare, get upto mark with Data science projects and create a project within my team, considering I have a super supportive manager. I am super duper stuck, hoping for some clarity as this has been eating my head for a month and I have spoken to too many people, it's as balanced as a toss of a coin. submitted by /u/Chattyyyee [link] [comments]

- Currently majoring in industrial engineering, thinking of switching to a data science majorby /u/TANMAN84444 (Data Science) on September 29, 2023 at 4:55 pm
Hi, I'm currently a freshman in industrial engineering and have recently been questioning if it's right for me. I like the math (basically the main reason I went into it), but I have always struggled with science material and conceptual thinking--took two physics classes in high school and felt like I still didn't understand it. I was recommended to go into data by people I've talked to and my advisor because it uses a lot of math that I like. I took two coding classes in high school, C++ and Python. I didn't overly love them, but I didn't hate them either, so I'm unsure about the coding element of the degree and job. My questions: Do you have an data science degree and what was your experience in college? What sort of jobs can you get with a data science degree? What does a job in data science actually look like? (I haven't found a good answer to that). How similar is this field to computer science? Those aren't all my concerns, but what I can think of right now. Any help would be appreciated. Thank you submitted by /u/TANMAN84444 [link] [comments]

- Bit of guidance?by /u/el_chubinebrae (Data Science) on September 29, 2023 at 4:43 pm
I've made some XgBoost models and found some good hyperparameter combinations to get some fairly decent results with my criss fold validations. I think the highest I've got is about 85% In real life it's showing signs of overfitting dropping to 55%. I'm trying to predict stock market direction, just up or down. But I have a train of thought that's leading down a rabbit hole I don't think I should be going down. I'm taking the latest prices along with some features and using that as my prediction row. Then I add another row of data and retrain the model with the same params again and predict, repeating about 180 times until I have an entire columns of predictions. I understand it's computationally expensive to repeat this process so many time, it doesn't take a great deal of time to do it. I thought if I use the data from the training set then I'll suffer from Overfitting, which I clearly am already doing so but I'll carry on trying to reduce overfitting. Should I trim the training set to a point before the dates I want to predict and use the same model for these 180 days? Or should I think about retraining the model every 30 or so data points? I feel like there's almost limitless possibilities and I've gone down the wrong path which will render everything I've done up till now pointless. submitted by /u/el_chubinebrae [link] [comments]

- What the Birthday Paradox Teaches Us About Protecting Patron Privacyby /u/ravy (Data Science) on September 29, 2023 at 4:26 pm
submitted by /u/ravy [link] [comments]

- First project review | Data wrangling and Visualizationby /u/Alarming_Scene126 (Data Science) on September 29, 2023 at 4:17 pm
Hello guys, This is my first project and i request you guys to please check out my work, leave a comment on what i can improve and upvote in kaggle it you like it. I have performed: • Data manipulation (pandas, numpy) • Data visualization (pandasql, matplotlib) I would like to thank this community for creating opportunity for ppl like us to share our work. Thank you all!! submitted by /u/Alarming_Scene126 [link] [comments]

- [D][R] Deploying deep models on memory constrained devicesby /u/jasio1909 (Machine Learning) on September 29, 2023 at 4:14 pm
Suppose we want to use a deep learning model on a gpu within our app. We want this model to coexist on the gpu with other processes, effectively limit it's possible usage of resources. As cuDNN/cuBLAS routines are nondeterministic and possibly dynamically allocate variable amount of memory, how do people manage this problem? Is it a problem at all? Estimating memory usage of deep learning models on gpu is notoriously hard. There is a research paper from Microsoft tackling this problem and they mispredict the usage of memory by 15% on average. Some cpu BLAS libraries like openBLAS or MKL also dynamically allocate the memory, but there are alternatives - LAPACK as far as I know uses only the memory provided by the caller, making it viable option for applications in embedded. In safety criticall tasks like autonomous driving, it seems to be especially important to have deterministic and clear bounds on memory usage of the process and not get spontaneously hit by CUDA OOM error. I can imagine that for autonomous vehicles, the prediction pipeline usually is the only process occupying the GPU, making the problem less visible or go away completely. In case of desktop applications only running the inference, the problem is also less visible as the memory requirements for forward pass only are comparatively low (we can reuse allocated memory blocks efficiently). However, I am looking on this subject through the problem of training/finetuning deep models on the edge devices, being increasingly available thing to do. Looking at tflite, alibaba's MNN, mit-han-lab's tinyengine etc.. To summarize: 1. Do nondeterministic memory allocations pose a problem for deploying deep models in the wild and if so, what strategies do people employ to mitigate this problem? 2. Do you think it would be beneficial to have a deep learning library with worse performance but with fine graned controll over the memory allocations? (If such library doesn't already exist. If it does, please tell me.) Such a library could possibly enable you to choose from a list of possible computation routines, providing you with required memory before the call is made and choose suitable perf/memory tradeoff routine for a given state of the machine per function call. Eg: if os.free_mem>matmul(x,y,fast).mem_cost: matmul(x,y,fast).compute() else: matmul(x,y,economic).compute() submitted by /u/jasio1909 [link] [comments]

- [D] Best Sequence Embedding Models?by /u/Uilxitora (Machine Learning) on September 29, 2023 at 3:04 pm
Which are currently the best Sentence Embedding pre-trained models out there? submitted by /u/Uilxitora [link] [comments]

- Last Call for RUGS Grant Applications!by /u/Interesting_Chance31 (Data Science) on September 29, 2023 at 2:55 pm
Hello to all R enthusiast, just a friendly reminder to anyone eyeing the RUGS grant opportunity. The clock's ticking with the deadline set for tomorrow, September 30th, 2023. Don't miss out on this chance to bolster your R-based projects. All details are here: https://www.r-consortium.org/all-projects/r-user-group-support-program. Seize the moment! submitted by /u/Interesting_Chance31 [link] [comments]