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

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

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.

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

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

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

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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.


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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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  • Minimum tenure at a company
    by /u/ergodym (Data Science) on July 26, 2024 at 5:51 pm

    What do you consider a minimum tenure to be at a company before deciding it's time to move on? When is too early as opposed to still try hard to change opinion. Specifically related to DS rols. submitted by /u/ergodym [link] [comments]

  • How do you find use cases for data science in an organization?
    by /u/cptsanderzz (Data Science) on July 26, 2024 at 3:15 pm

    I know most people say “find a problem then use data science to solve it” but my question is how do people find these problems? Throughout my minimal career of 3 years as a data scientist the vast majority of problems can be solved using data analysis, how do you find opportunities to utilize more sophisticated data science techniques? submitted by /u/cptsanderzz [link] [comments]

  • DS in product analytics, what are your low hanging fruits when entering a new job or project that brought the most impact
    by /u/LibiSC (Data Science) on July 26, 2024 at 3:13 pm

    If you are no in product analytics more industry agnostic recommendations are welcome submitted by /u/LibiSC [link] [comments]

  • [D] Every annotator has a guidebook, but the reviewers don't
    by /u/Spico197 (Machine Learning) on July 26, 2024 at 1:20 pm

    I submitted to the ACL rolling review in June and found the reviewers' evaluation scores very subjective. Although the ACL committee has an instruction on some basic reviewing guidelines, there lacks of a preliminary test for the reviewers to explicitly show the evaluation standards. Maybe we should provide some paper-score examples to prompt the reviewers for more objective reviews? Or build a test before they make reviews to make sure they fully understand the meaning of soundness and overall assessment, rather than giving some random scores based on their personal interests. submitted by /u/Spico197 [link] [comments]

  • [D] How OpenAI JSON mode implemented?
    by /u/Financial_Air5256 (Machine Learning) on July 26, 2024 at 11:15 am

    I assume that all the training data is in JSON format, but higher temperature or other randomness during generation doesn’t guarantee that the outputs will always be in JSON. What other methods do you think could ensure that the outputs are consistently in JSON? Perhaps some rule-based methods during decoding could help? submitted by /u/Financial_Air5256 [link] [comments]

  • [D] Do only some hardware support int4 quantization? If so why?
    by /u/Abs0lute_Jeer0 (Machine Learning) on July 26, 2024 at 7:56 am

    I tried quantizing my finetuned mT5 model using the optimum’s openvino wrapper to int8 and int4. There was very little difference in the inference time, close to 5%. This makes me wonder if it’s an issue with hardware. I’m using intel sapphire rapids and it has an avx512_vnni instruction set. How did I figure out if it supports int4? And why and why not? submitted by /u/Abs0lute_Jeer0 [link] [comments]

  • [D] Normalization in transformers
    by /u/lostn4d (Machine Learning) on July 26, 2024 at 7:44 am

    After the first theoretical issue with my transformer, I now see another. The original paper uses normalization after residual addition (Post-LN), which led to training difficulties and later got replaced by normalization at the beginning of each attention or mlp block/branch (Pre-LN). This is known to work better in practice (trainable without warmup, restores highway effect), but it still doesn't seem completely ok theoretically. First consider things without normalization. Assuming attention and mlp blocks are properly set up and mostly keep norms, each residual addition would sum two similar norm signals, potentially scaling up by something like 1.4 (depending on correlation, but it starts at sqrt(2) after random init). So the norms after the blocks could look like this: [1(main)+1(residual)=1.4] -> [1.4+1.4=2] -> [2+2=2.8] etc. This would cause various problems (like changing the softmax temp in later attention blocks), so adjustment is needed. Pre-LN ensures each block works on normalized values (thus with constant - if slightly arbitrary - softmax temperature). But since it doesn't affect the norm of the main signal (as forwarded by the skip connection) but only the residual, the norms can still grow, albeit slower. The expectation is now roughly: [1+1=1.4] -> [1.4+1=1.7] -> [1.7+1=2] -> [2+1=2.2] etc - with a final normalization correcting the signal near output (Pre-LN paper). One possible issue with this is that later attention blocks may have reduced effect, as they add unit norm residuals to a potentially larger and larger main signal. What is the usual take on this problem? Can it be ignored in practice? Does Pre-LN work acceptably despite it, even for deep models (where the main norm discrepancy can grow larger)? There are lots of alternative normalization papers, but what is the practical consensus? Btw attention is extremely norm-sensitive (or, equivalently, the hidden temperature of softmax is critical). This is a sharp contrast to fc or convolution which are mostly scale-oblivious. For anybody interested: consider what happens when most raw attention dot products come out 0 (= query and key is orthogonal, no info from this context slot) with only one slot giving 1 (= positive affinity, after downscaled by sqrt(qk_siz) ). I for one got surprised by this during debug. submitted by /u/lostn4d [link] [comments]

  • What's the most interesting Data Science interview question you've encountered?
    by /u/NickSinghTechCareers (Data Science) on July 26, 2024 at 12:42 am

    What's the most interesting Data Science Interview question you've been asked? Bonus points if it: appears to be hard, but is actually easy appears to be simple, but is actually nuanced I'll go first – at a geospatial analytics startup, I was asked about how we could use location data to help McDonalds open up their next store location in an optimal spot. It was fun to riff about what features I'd use in my analysis, and potential downsides off each feature. I also got to show off my domain knowledge by mentioning some interesting retail analytics / credit-card spend datasets I'd also incorporate. This impressed the interviewer since the companies I mentioned were all potential customers/partners/competitors (it's a complicated ecosystem!). How about you – what's the most interesting Data Science interview question you've encountered? submitted by /u/NickSinghTechCareers [link] [comments]

  • [R] How do you search for implementations of Mixture of Expert models that can be trained locally in a laptop or desktop without ultra-high end GPUs?
    by /u/Furiousguy79 (Machine Learning) on July 25, 2024 at 11:12 pm

    Hi, I am a 2nd year PhD student in CS. My supervisor just got this idea about MoEs and fairness and asked me to implement it ( work on a toy classification problem on tabular data and NOT language data). However as it is not their area of expertise, they did not give any guidelines on how to approach it. My main question is: How do I search for or proceed with implementing a mixture of expert models? The ones that I find are for chatting and such but I mainly work with tabular EHR data. This is my first foray into this area (LLMs and MoEs) and I am kind of lost with all these Mixtral, openMoE, etc. As we do not have access to Google Collab or have powerful GPUs I have to rely on local training (My lab PC has 2080ti and my laptop has 4070). Any guideline or starting point on how to proceed would be greatly appreciated. submitted by /u/Furiousguy79 [link] [comments]

  • Seeking ML Solutions for Analyzing Player Movement in Field Sports
    by /u/vaalenz (Data Science) on July 25, 2024 at 10:40 pm

    Hi everyone! I'm working on a project where I have detailed information on player movements in field sports such as Soccer, Rugby, and Field Hockey. The dataset includes second-by-second data on player positions (latitude and longitude), speed, and heart rate. I’m looking for help with two specific objectives using machine learning: Detecting and Classifying Game Phases: I want to develop a system that can identify and classify different game phases like attacking, defending, counter-attacks, rest periods, etc. Automatically Splitting the Game into Quarters or Halves: Additionally, I need to automatically segment the game into quarters or halves, and determine the exact times these segments occur. I’d appreciate any suggestions on how to approach these problems. What algorithms or models would be best suited for these tasks? Are there any existing frameworks or tools that could be particularly useful?Thanks for your help!! submitted by /u/vaalenz [link] [comments]

  • What is it with jobs requiring a master’s AND a PhD?
    by /u/Rare_Art_9541 (Data Science) on July 25, 2024 at 8:11 pm

    I was looking through some postings On indeed. And I noticed that there are several data science postings that require both a master’s and a PhD. You’re telling me if you decide to skip a master’s and go straight for the PhD, you’re not considered qualified? submitted by /u/Rare_Art_9541 [link] [comments]

  • [P] How to make "Out-of-sample" Predictions
    by /u/Individual_Ad_1214 (Machine Learning) on July 25, 2024 at 7:47 pm

    My data is a bit complicated to describe so I'm going try to describe something analogous. Each example is randomly generated, but you can group them based on a specific but latent (by latent I mean this isn't added into the features used to develop a model, but I have access to it) feature (in this example we'll call this number of bedrooms). Feature x1 Feature x2 Feature x3 ... Output (Rent) Row 1 Row 2 Row 3 Row 4 Row 5 Row 6 Row 7 2 Row 8 1 Row 9 0 So I can group Row 1, Row 2, and Row 3 based on a latent feature called number of bedrooms (which in this case is 0 bedroom). Similarly, Row 4, Row 5, & Row 6 have 2 Bedrooms, and Row 7, Row 8, & Row 9 have 4 Bedrooms. Furthermore, these groups also have an optimum price which is used to create output classes (output here is Rent; increase, keep constant, or decrease). So say the optimum price for the 4 bedrooms group is $3mil, and row 7 has a price of $4mil (=> 3 - 4 = -1 mil, i.e a -ve value so convert this to class 2, or above optimum or increase rent), row 8 has a price of $3mil (=> 3 - 3 = 0, convert this to class 1, or at optimum), and row 9 has a price of $2mil (3 - 2 = 1, i.e +ve value, so convert this to class 0, or below optimum, or decrease rent). I use this method to create an output class for each example in the dataset (essentially, if example x has y number of bedrooms, I get the known optimum price for that number of bedrooms and I subtract the example's price from the optimum price). Say I have 10 features (e.g. square footage, number of bathrooms, parking spaces etc.) in the dataset, these 10 features provide the model with enough information to figure out the "number of bedrooms". So when I am evaluating the model, feature x1 feature x2 feature x3 ... Row 10 e.g. I pass into the model a test example (Row 10) which I know has 4 bedrooms and is priced at $6mil, the model can accurately predict class 2 (i.e increase rent) for this example. Because the model was developed using data with a representative number of bedrooms in my dataset. Features.... Output (Rent) Row 1 0 Row 2 0 Row 3 0 However, my problem arises at examples with a low number of bedrooms (i.e. 0 bedrooms). The input features doesn't have enough information to determine the number of bedrooms for examples with a low number of bedrooms (which is fine because we assume that within this group, we will always decrease the rent, so we set the optimum price to say $2000. So row 1 price could be $8000, (8000 - 2000 = 6000, +ve value thus convert to class 0 or below optimum/decrease rent). And within this group we rely on the class balance to help the model learn to make predictions because the proportion is heavily skewed towards class 0 (say 95% = class 0 or decrease rent, and 5 % = class 1 or class 2). We do this based the domain knowledge of the data (so in this case, we would always decrease the rent because no one wants to live in a house with 0 bedrooms). MAIN QUESTION: We now want to predict (or undertake inference) for examples with number of bedrooms in between 0 bedrooms and 2 bedrooms (e.g 1 bedroom NOTE: our training data has no example with 1 bedroom). What I notice is that the model's predictions on examples with 1 bedroom act as if these examples had 0 bedrooms and it mostly predicts class 0. My question is, apart from specifically including examples with 1 bedroom in my input data, is there any other way (more statistics or ML related way) for me to improve the ability of my model to generalise on unseen data? submitted by /u/Individual_Ad_1214 [link] [comments]

  • Does every new data science job get boring after a couple years?
    by /u/Lamp_Shade_Head (Data Science) on July 25, 2024 at 7:26 pm

    I am in my second job after grad school and am noticing a pattern in how I feel about my job as time goes on. In my first job, I felt bored and restless around the 1.5-year mark and eventually left. Now, after 2.5 years at my current job, I find myself feeling bored and disinterested again. I fulfill my responsibilities and do them well, but I no longer go above and beyond as I did in the first year. Is it unusual to feel this way, or is it normal? submitted by /u/Lamp_Shade_Head [link] [comments]

  • [R] EMNLP Paper review scores
    by /u/Immediate-Hour-8466 (Machine Learning) on July 25, 2024 at 7:06 pm

    EMNLP paper review scores Overall assessment for my paper is 2, 2.5 and 3. Is there any chance that it may still be selected? The confidence is 2, 2.5 and 3. The soundness is 2, 2.5, 3.5. I am not sure how soundness and confidence may affect my paper's selection. Pls explain how this works. Which metrics should I consider important. Thank you! submitted by /u/Immediate-Hour-8466 [link] [comments]

  • Using Kriging interpolation on 2D slices of 3D data
    by /u/RandomFactChecker_ (Data Science) on July 25, 2024 at 6:52 pm

    Edit: Added image of the dataset I am working on which can be seen on the top left where the kriging perdiction is on the top right. I'm working on interpolating 2D data slices from a 3D grid at a specific point. If I take slices around that point in various directions, can I average the kriging values from these different slices to obtain a single overall 3D kriging value for that point? Would doing this ruin the values outputted by the Kinging interpolation and make them have greater error? If I can take this approach what would be the best approach to ensure accuracy in this interpolation process? The dataset I am working on which can be seen on the top left where the kriging prediction is on the top right. To be more specific the database I am using is one I created myself which is filled with wind speed, direction and variance at each lat lon point at 0.25 resolution. I am doing this for alts 15 000 - 30 000 meters however as seen there is gaps in the data. I am trying to use kriging to fill in these gaps. In the photo below I am only doing one slice of data at lon = -179 so I can use 2D kriging but I am wondering if I can do the averaging around each point to something closer to a 3D kring. I am also doing this because I have a working 2D kriging add on for MATLAB that has good documentation but cant find a good one for 3D. The https://preview.redd.it/3rwti6ip4wed1.png?width=1038&format=png&auto=webp&s=a0cbce4a84d551f03f9b2c657f4153987661f4a2 submitted by /u/RandomFactChecker_ [link] [comments]

  • [N] OpenAI announces SearchGPT
    by /u/we_are_mammals (Machine Learning) on July 25, 2024 at 6:41 pm

    https://openai.com/index/searchgpt-prototype/ We’re testing SearchGPT, a temporary prototype of new AI search features that give you fast and timely answers with clear and relevant sources. submitted by /u/we_are_mammals [link] [comments]

  • [P] Local Llama 3.1 and Marqo Retrieval Augmented Generation
    by /u/elliesleight (Machine Learning) on July 25, 2024 at 4:45 pm

    I built a simple starter demo of a Knowledge Question and Answering System using Llama 3.1 (8B GGUF) and Marqo. Feel free to experiment and build on top of this yourselves! GitHub: https://github.com/ellie-sleightholm/marqo-llama3_1 submitted by /u/elliesleight [link] [comments]

  • [N] AI achieves silver-medal standard solving International Mathematical Olympiad problems
    by /u/we_are_mammals (Machine Learning) on July 25, 2024 at 4:16 pm

    https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/ They solved 4 of the 6 IMO problems (although it took days to solve some of them). This would have gotten them a score of 28/42, just one point below the gold-medal level. submitted by /u/we_are_mammals [link] [comments]

  • [R] Explainability of HuggingFace Models (LLMs) for Text Summarization/Generation Tasks
    by /u/PhoenixHeadshot25 (Machine Learning) on July 25, 2024 at 3:19 pm

    Hi community, I am exploring the Responsible AI domain where I have started reading about methods and tools to make Deep Learning Models explainable. I have already used SHAP and LIMe for ML model explainability. However, I am unsure about their use in explaining LLMs. I know that these methods are model agnostic but can we use these methods for Text Generation or Summarization tasks? I got reference docs from Shap explaining GPT2 for text generation tasks, but I am unsure about using it for other newer LLMs. Additionally, I would like to know, are there any better ways for Explainable AI for LLMs? submitted by /u/PhoenixHeadshot25 [link] [comments]

  • Worth it to take a pay cut for the data scientist title?
    by /u/son_of_tv_c (Data Science) on July 25, 2024 at 3:17 pm

    I have an MS in stats and 7 years as an analyst under my belt. I've been looking for a data scientist jb ever since I got the MS 4 years ago (got it part time while I started as an analyst) and have been having a hell of a time at it. I get plenty of interest in analyst positoins, but little interest in data scientist positoins. As I'm sure you all know, there is considerable overlap between the titles but HR drones and ATS doesn't necessarily know this. All they care about is key words. I've been offered a data scientist positoin at a company that I am ready to accept. The positoin is a little underpaid for a DS but about enough for me right now, but I'm thinking it could be a great stepping stone. I work that for 2-3 years then I'm competitive for higher compensated DS positoins. However I just got off the phone with a recriuter for a DA positoin that would pay between 25-40k more than the DS positoin (it's just a band at this point). The responsibilities are similar, it's just that this place has more money and is located in a HCOL are (both are remote though so COL and relocating are not a factor for me). More money now would be great, but I don't really know if this is going to leave me in a better position in a few years. Obviously, we're talking an offer vs just one phone screen, the higher DA positoin isn't a sure thing right now. But I'm just wondering if you guys would even keep pursing the DA positoin or just take the DS positoin and make up the difference in a few years with a higher paid DS positoin? Also I hate that this is a factor but I've done 12 interveiws just this month, I really REALLY don't want to do anymore, so it's a huge factor in me wanting to just drop out of the DA interveiw process and take the DS. submitted by /u/son_of_tv_c [link] [comments]

 

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