![Revisit consent button](../images/body-df29beacd7496220cc94.svg) We value your privacy We use cookies to enhance your browsing experience, serve personalised ads or content, and analyse our traffic. By clicking "Accept All", you consent to our use of cookies. Customise Reject All Accept All Customise Consent Preferences ![](../images/body-2159bb67f3de8ad870eb.svg) We use cookies to help you navigate efficiently and perform certain functions. You will find detailed information about all cookies under each consent category below. The cookies that are categorised as "Necessary" are stored on your browser as they are essential for enabling the basic functionalities of the site. ... Show more NecessaryAlways Active Necessary cookies are required to enable the basic features of this site, such as providing secure log-in or adjusting your consent preferences. These cookies do not store any personally identifiable data. * Cookie BCTempID * Duration 10 minutes * Description No description available. * Cookie __cf_bm * Duration 1 hour * Description This cookie, set by Cloudflare, is used to support Cloudflare Bot Management. * Cookie AWSALBCORS * Duration 7 days * Description Amazon Web Services set this cookie for load balancing. * Cookie _cfuvid * Duration session * Description Cloudflare sets this cookie to track users across sessions to optimize user experience by maintaining session consistency and providing personalized services * Cookie li_gc * Duration 6 months * Description Linkedin set this cookie for storing visitor's consent regarding using cookies for non-essential purposes. * Cookie __hssrc * Duration session * Description This cookie is set by Hubspot whenever it changes the session cookie. The __hssrc cookie set to 1 indicates that the user has restarted the browser, and if the cookie does not exist, it is assumed to be a new session. * Cookie __hssc * Duration 1 hour * Description HubSpot sets this cookie to keep track of sessions and to determine if HubSpot should increment the session number and timestamps in the __hstc cookie. * Cookie wpEmojiSettingsSupports * Duration session * Description WordPress sets this cookie when a user interacts with emojis on a WordPress site. It helps determine if the user's browser can display emojis properly. * Cookie BCSessionID * Duration 1 year 1 month 4 days * Description Blueconic sets this cookie as a unique identifier for the BlueConic profile. * Cookie _octo * Duration 1 year * Description No description available. * Cookie logged_in * Duration 1 year * Description No description available. * Cookie __Secure-YEC * Duration past * Description YouTube sets this cookie to stores the user's video player preferences using embedded YouTube video * Cookie __eoi * Duration 6 months * Description Description is currently not available. * Cookie AWSALBTGCORS * Duration 7 days * Description No description available. * Cookie login-status-p * Duration past * Description Description is currently not available. * Cookie AWSALBTG * Duration 7 days * Description No description available. * Cookie csrf_token * Duration session * Description No description available. * Cookie token_v2 * Duration 1 day * Description Description is currently not available. * Cookie D * Duration 1 year * Description Description is currently not available. * Cookie PHPSESSID * Duration session * Description This cookie is native to PHP applications. The cookie stores and identifies a user's unique session ID to manage user sessions on the website. The cookie is a session cookie and will be deleted when all the browser windows are closed. * Cookie VISITOR_PRIVACY_METADATA * Duration 6 months * Description YouTube sets this cookie to store the user's cookie consent state for the current domain. * Cookie cookietest * Duration session * Description The cookietest cookie is typically used to determine whether the user's browser accepts cookies, essential for website functionality and user experience. * Cookie __Host-airtable-session * Duration 1 year * Description This cookie is used to enable us to integrate the services of Airtable. * Cookie __Host-airtable-session.sig * Duration 1 year * Description This cookie is used to enable us to integrate the services of Airtable. * Cookie m * Duration 1 year 1 month 4 days * Description Stripe sets this cookie for fraud prevention purposes. It identifies the device used to access the website, allowing the website to be formatted accordingly. * Cookie BIGipServer* * Duration session * Description Marketo sets this cookie to collect information about the user's online activity and build a profile about their interests to provide advertisements relevant to the user. * Cookie __cfruid * Duration session * Description Cloudflare sets this cookie to identify trusted web traffic. * Cookie _GRECAPTCHA * Duration 6 months * Description Google Recaptcha service sets this cookie to identify bots to protect the website against malicious spam attacks. * Cookie __Secure-YNID * Duration 6 months * Description Google cookie used to protect user security and prevent fraud, especially during the login process. * Cookie cookieyes-consent * Duration 1 year * Description CookieYes sets this cookie to remember users' consent preferences so that their preferences are respected on subsequent visits to this site. It does not collect or store any personal information about the site visitors. Functional Functional cookies help perform certain functionalities like sharing the content of the website on social media platforms, collecting feedback, and other third-party features. * Cookie lidc * Duration 1 day * Description LinkedIn sets the lidc cookie to facilitate data center selection. * Cookie brw * Duration 1 year * Description No description available. * Cookie brwConsent * Duration 5 minutes * Description Description is currently not available. * Cookie WMF-Uniq * Duration 1 year * Description Description is currently not available. * Cookie loom_anon_comment * Duration 1 year * Description No description available. * Cookie loom_referral_video * Duration session * Description Description is currently not available. * Cookie VISITOR_INFO1_LIVE * Duration 6 months * Description A cookie set by YouTube to measure bandwidth that determines whether the user gets the new or old player interface. * Cookie yt-remote-connected-devices * Duration Never Expires * Description YouTube sets this cookie to store the user's video preferences using embedded YouTube videos. * Cookie ytidb::LAST_RESULT_ENTRY_KEY * Duration Never Expires * Description The cookie ytidb::LAST_RESULT_ENTRY_KEY is used by YouTube to store the last search result entry that was clicked by the user. This information is used to improve the user experience by providing more relevant search results in the future. * Cookie yt-remote-device-id * Duration Never Expires * Description YouTube sets this cookie to store the user's video preferences using embedded YouTube videos. * Cookie yt-remote-session-name * Duration session * Description The yt-remote-session-name cookie is used by YouTube to store the user's video player preferences using embedded YouTube video. * Cookie yt-remote-fast-check-period * Duration session * Description The yt-remote-fast-check-period cookie is used by YouTube to store the user's video player preferences for embedded YouTube videos. * Cookie yt-remote-session-app * Duration session * Description The yt-remote-session-app cookie is used by YouTube to store user preferences and information about the interface of the embedded YouTube video player. * Cookie yt-remote-cast-available * Duration session * Description The yt-remote-cast-available cookie is used to store the user's preferences regarding whether casting is available on their YouTube video player. * Cookie yt-remote-cast-installed * Duration session * Description The yt-remote-cast-installed cookie is used to store the user's video player preferences using embedded YouTube video. * Cookie cp_session * Duration 3 months * Description Codepen sets this cookie for Help systems found in the website. * Cookie loid * Duration 1 year 1 month 4 days * Description This cookie is set by the Reddit. The cookie enables the sharing of content from the website onto the social media platform. Analytics Analytical cookies are used to understand how visitors interact with the website. These cookies help provide information on metrics such as the number of visitors, bounce rate, traffic source, etc. * Cookie __hstc * Duration 6 months * Description Hubspot set this main cookie for tracking visitors. It contains the domain, initial timestamp (first visit), last timestamp (last visit), current timestamp (this visit), and session number (increments for each subsequent session). * Cookie hubspotutk * Duration 6 months * Description HubSpot sets this cookie to keep track of the visitors to the website. This cookie is passed to HubSpot on form submission and used when deduplicating contacts. * Cookie _ga * Duration 1 year 1 month 4 days * Description Google Analytics sets this cookie to calculate visitor, session and campaign data and track site usage for the site's analytics report. The cookie stores information anonymously and assigns a randomly generated number to recognise unique visitors. * Cookie _ga_* * Duration 1 year 1 month 4 days * Description Google Analytics sets this cookie to store and count page views. * Cookie __Host-psifi.analyticsTrace * Duration 6 hours * Description Description is currently not available. * Cookie __Host-psifi.analyticsTraceV2 * Duration 6 hours * Description Description is currently not available. * Cookie _gh_sess * Duration session * Description GitHub sets this cookie for temporary application and framework state between pages like what step the user is on in a multiple step form. * Cookie YSC * Duration session * Description YSC cookie is set by Youtube and is used to track the views of embedded videos on Youtube pages. * Cookie ajs_anonymous_id * Duration 1 year * Description This cookie is set by Segment to count the number of people who visit a certain site by tracking if they have visited before. * Cookie vuid * Duration 1 year 1 month 4 days * Description Vimeo installs this cookie to collect tracking information by setting a unique ID to embed videos on the website. Performance Performance cookies are used to understand and analyse the key performance indexes of the website which helps in delivering a better user experience for the visitors. * Cookie AWSALB * Duration 7 days * Description AWSALB is an application load balancer cookie set by Amazon Web Services to map the session to the target. * Cookie acq * Duration past * Description Description is currently not available. * Cookie acq.sig * Duration past * Description Description is currently not available. * Cookie ptc * Duration 2 years * Description No description available. Advertisement Advertisement cookies are used to provide visitors with customised advertisements based on the pages you visited previously and to analyse the effectiveness of the ad campaigns. * Cookie muc_ads * Duration 1 year 1 month 4 days * Description Twitter sets this cookie to collect user behaviour and interaction data to optimize the website. * Cookie guest_id_marketing * Duration 1 year 1 month 4 days * Description Twitter sets this cookie to identify and track the website visitor. * Cookie guest_id_ads * Duration 1 year 1 month 4 days * Description Twitter sets this cookie to identify and track the website visitor. * Cookie personalization_id * Duration 1 year 1 month 4 days * Description Twitter sets this cookie to integrate and share features for social media and also store information about how the user uses the website, for tracking and targeting. * Cookie guest_id * Duration 1 year 1 month 4 days * Description Twitter sets this cookie to identify and track the website visitor. It registers if a user is signed in to the Twitter platform and collects information about ad preferences. * Cookie bcookie * Duration 1 year * Description LinkedIn sets this cookie from LinkedIn share buttons and ad tags to recognize browser IDs. * Cookie __Secure-ROLLOUT_TOKEN * Duration 6 months * Description YouTube sets this cookie to manage feature rollout and experimentation. It helps Google control which new features or interface changes are shown to users as part of testing and staged rollouts, ensuring consistent experience for a given user during an experiment. * Cookie yt.innertube::nextId * Duration Never Expires * Description YouTube sets this cookie to register a unique ID to store data on what videos from YouTube the user has seen. * Cookie yt.innertube::requests * Duration Never Expires * Description YouTube sets this cookie to register a unique ID to store data on what videos from YouTube the user has seen. * Cookie session_tracker * Duration session * Description This cookie is set by the Reddit. This cookie is used to identify trusted web traffic. It also helps in adverstising on the website. * Cookie edgebucket * Duration session * Description Reddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content. * Cookie did * Duration 1 year * Description Arbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year. Uncategorised Other uncategorised cookies are those that are being analysed and have not been classified into a category as yet. No cookies to display. Reject All Save My Preferences Accept All Toggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation [](https://towardsdatascience.com/) Publish AI, ML & data-science insights to a global community of data professionals. Sign in[Submit an Article](https://write.insightmediagroup.io) [Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/) * * * [Write For TDS](https://towardsdatascience.com/submissions/) [LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search [Data Science](https://towardsdatascience.com/category/data-science/) # When Predictors Collide: Mastering VIF in Multicollinear Regression Explore how the Variance Inflation Factor helps detect and manage multicollinearity in your regression models. [Niklas Lang](https://towardsdatascience.com/author/niklas_lang/) April 16, 20259 min read ![](../images/000.jpg) [Photo](https://unsplash.com/photos/a-blurry-photo-of-a-city-at-night-KFQPK9Pow5k) by MARIOLA GROBELSKA via Unsplash In regression models, the independent variables must be not or only slightly dependent on each other, i.e. that they are not correlated. However, if such a dependency exists, this is referred to as multicollinearity and leads to unstable models and results that are difficult to interpret. The variance inflation factor is a decisive metric for recognizing multicollinearity and indicates the extent to which the correlation with other predictors increases the variance of a regression coefficient. A high value of this metric indicates a high correlation of the variable with other independent variables in the model. In the following article, we look in detail at multicollinearity and the VIF as a measurement tool. We also show how the VIF can be interpreted and what measures can be taken to reduce it. We also compare the indicator with other methods for measuring multicollinearity. ## What is Multicollinearity? [Multicollinearity](https://databasecamp.de/en/statistics/multicollinearity) is a phenomenon that occurs in regression analysis when two or more variables are strongly correlated with each other so that a change in one variable leads to a change in the other variable. As a result, the development of an independent variable can be predicted completely or at least partially by another variable. This complicates the prediction of linear regression to determine the influence of an independent variable on the dependent variable. A distinction can be made between two types of multicollinearity: Learn this step by step with the interactive [AI and Data Scientist](https://roadmap.sh/ai-data-scientist) roadmap. * **Perfect Multicollinearity** : a variable is an exact linear combination of another variable, for example when two variables measure the same thing in different units, such as weight in kilograms and pounds. * **High Degree of Multicollinearity** : Here, one variable is strongly, but not completely, explained by at least one other variable. For example, there is a high correlation between a person's education and their income, but it is not perfect multicollinearity. The occurrence of multicollinearity in regressions leads to serious problems as, for example, the regression coefficients become unstable and react very strongly to new data, so that the overall prediction quality suffers. Various methods can be used to recognize multicollinearity, such as the correlation matrix or the variance inflation factor, which we will look at in more detail in the next section. ## What is the Variance Inflation Factor (VIF)? The variance inflation factor (VIF) describes a diagnostic tool for regression models that helps to detect multicollinearity. It indicates the factor by which the variance of a coefficient increases due to the correlation with other variables. A high VIF value indicates a strong multicollinearity of the variable with other independent variables. This negatively influences the regression coefficient estimate and results in high standard errors. It is therefore important to calculate the VIF so that multicollinearity is recognized at an early stage and countermeasures can be taken. The VIF for a single variable iii is calculated using this formula: [latex] \\[VIF = \frac{1}{(1 - R^2)}\\] Here R2R^2R2 is the so-called coefficient of determination of the regression of feature iii against all other independent variables. A high R2R^2R2 value indicates that a large proportion of the variables can be explained by the other features, so that multicollinearity is suspected. In a regression with the three independent variables X1X_1X1​, X2X_2X2​ and X3X_3X3​, for example, one would train a regression with X1X_1X1​ as the dependent variable and X2X_2X2​ and X3X_3X3​ as independent variables. With the help of this model, R12R_{1}^2R12​ could then be calculated and inserted into the formula for the VIF. This procedure would then be repeated for the remaining combinations of the three independent variables. A typical threshold value is VIF > 10, which indicates strong multicollinearity. In the following section, we look in more detail at the interpretation of the variance inflation factor. ## How can different Values of the Variance Inflation Factor be interpreted? After calculating the VIF, it is important to be able to evaluate what statement the value makes about the situation in the model and to be able to deduce whether measures are necessary. The values can be interpreted as follows: * **VIF = 1** : This value indicates that there is no multicollinearity between the analyzed variable and the other variables. This means that no further action is required. * **VIF between 1 and 5** : If the value is in the range between 1 and 5, then there is multicollinearity between the variables, but this is not large enough to represent an actual problem. Rather, the dependency is still moderate enough that it can be absorbed by the model itself. * **VIF > 5**: In such a case, there is already a high degree of multicollinearity, which requires intervention in any case. The standard error of the predictor is likely to be significantly excessive, so the regression coefficient may be unreliable. Consideration should be given to combining the correlated predictors into one variable. * **VIF > 10**: With such a value, the variable has serious multicollinearity and the regression model is very likely to be unstable. In this case, consideration should be given to removing the variable to obtain a more powerful model. Overall, a high VIF value indicates that the variable may be redundant, as it is highly correlated with other variables. In such cases, various measures should be taken to reduce multicollinearity. ## What measures help to reduce the VIF? There are various ways to circumvent the effects of multicollinearity and thus also reduce the variance inflation factor. The most popular measures include: * **Removing highly correlated variables** : Especially with a high VIF value, removing individual variables with high multicollinearity is a good tool. This can improve the results of the regression, as redundant variables estimate the coefficients more unstable. * [**Principal component analysis (PCA)**](https://databasecamp.de/en/statistics/principal-component-analysis-en): The core idea of principal component analysis is that several variables in a data set may measure the same thing, i.e. be correlated. This means that the various dimensions can be combined into fewer so-called principal components without compromising the significance of the data set. Height, for example, is highly correlated with shoe size, as tall people often have taller shoes and vice versa. This means that the correlated variables are then combined into uncorrelated main components, which reduces multicollinearity without losing important information. However, this is also accompanied by a loss of interpretability, as the principal components do not represent real characteristics, but a combination of different variables. * **Regularization Methods** : Regularization comprises various methods that are used in statistics and machine learning to control the complexity of a model. It helps to react robustly to new and unseen data and thus enables the generalizability of the model. This is achieved by adding a penalty term to the model's optimization function to prevent the model from adapting too much to the training data. This approach reduces the influence of highly correlated variables and lowers the VIF. At the same time, however, the accuracy of the model is not affected. These methods can be used to effectively reduce the VIF and combat multicollinearity in a regression. This makes the results of the model more stable and the standard error can be better controlled. ## How does the VIF compare to other methods? The variance inflation factor is a widely used technique to measure multicollinearity in a data set. However, other methods can offer specific advantages and disadvantages compared to the VIF, depending on the application. ### **Correlation Matrix** The [correlation matrix](https://databasecamp.de/en/ml/correlation-matrix) is a statistical method for quantifying and comparing the relationships between different variables in a data set. The pairwise correlations between all combinations of two variables are shown in a tabular structure. Each cell in the matrix contains the so-called correlation coefficient between the two variables defined in the column and the row. This value can be between -1 and 1 and provides information on how the two variables relate to each other. A positive value indicates a positive correlation, meaning that an increase in one variable leads to an increase in the other variable. The exact value of the correlation coefficient provides information on how strongly the variables move about each other. With a negative correlation coefficient, the variables move in opposite directions, meaning that an increase in one variable leads to a decrease in the other variable. Finally, a coefficient of 0 indicates that there is no correlation. ![](../images/001.png) Example of a Correlation Matrix | Source: Author A correlation matrix therefore fulfills the purpose of presenting the correlations in a data set in a quick and easy-to-understand way and thus forms the basis for subsequent steps, such as model selection. This makes it possible, for example, to recognize multicollinearity, which can cause problems with regression models, as the parameters to be learned are distorted. Compared to the VIF, the correlation matrix only offers a surface analysis of the correlations between variables. However, the biggest difference is that the correlation matrix only shows the pairwise comparisons between variables and not the simultaneous effects between several variables. In addition, the VIF is more useful for quantifying exactly how much multicollinearity affects the estimate of the coefficients. ### Eigenvalue Decomposition Eigenvalue decomposition is a method that builds on the correlation matrix and mathematically helps to identify multicollinearity. Either the correlation matrix or the covariance matrix can be used. In general, small eigenvalues indicate a stronger, linear dependency between the variables and are therefore a sign of multicollinearity. Compared to the VIF, the eigenvalue decomposition offers a deeper mathematical analysis and can in some cases also help to detect multicollinearity that would have remained hidden by the VIF. However, this method is much more complex and difficult to interpret. The VIF is a simple and easy-to-understand method for detecting multicollinearity. Compared to other methods, it performs well because it allows a precise and direct analysis that is at the level of the individual variables. ## How to detect Multicollinearity in Python? Recognizing multicollinearity is a crucial step in data preprocessing in machine learning to train a model that is as meaningful and robust as possible. In this section, we therefore take a closer look at how the VIF can be calculated in Python and how the correlation matrix is created. ### Calculating the Variance Inflation Factor in Python The variance inflation factor can be easily used and imported in Python via the `statsmodels` library. Assuming we already have a Pandas DataFrame in a variable `X` that contains the independent variables, we can simply create a new, empty DataFrame for calculating the VIFs. The variable names and values are then saved in this frame. ![Collinearity](../images/002.png) A new row is created for each independent variable in `X` in the `Variable` column. It is then iterated through all variables in the data set and the variance inflation factor is calculated for the values of the variables and again saved in a list. This list is then stored as column VIF in the DataFrame. ### Calculating the Correlation Matrix In Python, a correlation matrix can be easily calculated using Pandas and then visualized as a heatmap using Seaborn. To illustrate this, we generate random data using NumPy and store it in a DataFrame. As soon as the data is stored in a DataFrame, the correlation matrix can be created using the `corr()` function. If no parameters are defined within the function, the Pearson coefficient is used by default to calculate the correlation matrix. Otherwise, you can also define a different correlation coefficient using the method parameter. ![Correlation Matrix / Korrelationsmatrix](../images/003.png) Finally, the heatmap is visualized using `seaborn`. To do this, the `heatmap()` function is called and the correlation matrix is passed. Among other things, the parameters can be used to determine whether the labels should be added and the color palette can be specified. The diagram is then displayed with the help of `matplolib`. ## This is what you should take with you * The variance inflation factor is a key indicator for recognizing multicollinearity in a regression model. * The coefficient of determination of the independent variables is used for the calculation. Not only the correlation between two variables can be measured, but also combinations of variables. * In general, a reaction should be taken if the VIF is greater than five, and appropriate measures should be introduced. For example, the affected variables can be removed from the data set or the principal component analysis can be performed. * In Python, the VIF can be calculated directly using statsmodels. To do this, the data must be stored in a DataFrame. The correlation matrix can also be calculated using Seaborn to detect multicollinearity. ## Register Now to Continue Reading ### Unlock Towards Data Science with a Free Account All articles on Towards Data Science are available to registered users. Create a free account today to access this article and thousands more. Register for freeSign in to your account * * * ![](../images/body-d123f8ba604c7f334425.jpeg) Written By ## [Niklas Lang](https://towardsdatascience.com/author/niklas_lang/) [See all from Niklas Lang](https://towardsdatascience.com/author/niklas_lang/) [Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Multicollinearity](https://towardsdatascience.com/tag/multicollinearity/)[Python](https://towardsdatascience.com/tag/python/)[Statistics](https://towardsdatascience.com/tag/statistics/)[Variance Inflation Factor](https://towardsdatascience.com/tag/variance-inflation-factor/) Share This Article * [](https://www.facebook.com/sharer/sharer.php?u=https%3A%2F%2Ftowardsdatascience.com%2Fwhen-predictors-collide-mastering-vif-in-multicollinear-regression%2F&title=When%20Predictors%20Collide%3A%20Mastering%20VIF%20in%20Multicollinear%20Regression) * [](https://www.linkedin.com/shareArticle?mini=true&url=https%3A%2F%2Ftowardsdatascience.com%2Fwhen-predictors-collide-mastering-vif-in-multicollinear-regression%2F&title=When%20Predictors%20Collide%3A%20Mastering%20VIF%20in%20Multicollinear%20Regression) * [](https://x.com/share?url=https%3A%2F%2Ftowardsdatascience.com%2Fwhen-predictors-collide-mastering-vif-in-multicollinear-regression%2F&text=When%20Predictors%20Collide%3A%20Mastering%20VIF%20in%20Multicollinear%20Regression) Towards Data Science is a community publication. Submit your insights to reach our global audience and earn through the TDS Author Payment Program. [Write for TDS](https://towardsdatascience.com/submissions/) ## Related Articles * [![](../images/004.jpeg)](https://towardsdatascience.com/a-series-on-flask-apis-part-1-getting-and-posting-33985dfe8816/) ## [A Series on Flask APIs, Part 1: GETting and POSTing](https://towardsdatascience.com/a-series-on-flask-apis-part-1-getting-and-posting-33985dfe8816/) [Programming](https://towardsdatascience.com/category/programming/) A how-to on GETting and POSTing data to a Flask API [Alexis McKenzie](https://towardsdatascience.com/author/lexmckenz/) August 23, 20214 min read * [![](../images/005.jpeg)](https://towardsdatascience.com/web-scraping-with-scrapy-theoretical-understanding-f8639a25d9cd/) ## [Web scraping with Scrapy: Theoretical Understanding](https://towardsdatascience.com/web-scraping-with-scrapy-theoretical-understanding-f8639a25d9cd/) [](https://towardsdatascience.com/when-predictors-collide-mastering-vif-in-multicollinear-regression/) This is the first part of a 4 part tutorial series on web scraping using Scrapy and Selenium. [Karthikeyan P](https://towardsdatascience.com/author/karthikn2789/) July 31, 202014 min read * [![](../images/006.jpg)](https://towardsdatascience.com/understand-the-workings-of-black-box-models-with-lime-92203f906431/) ## [Understand the Workings of Black-Box models with LIME](https://towardsdatascience.com/understand-the-workings-of-black-box-models-with-lime-92203f906431/) [Artificial Intelligence](https://towardsdatascience.com/category/artificial-intelligence/) While the performance of a machine learning model can seem impressive, it might not be making a significant impact to the business unless... [Suhas Maddali](https://towardsdatascience.com/author/suhas-maddali007/) August 3, 20228 min read * [![](../images/007.gif)](https://towardsdatascience.com/nearest-neighbor-analysis-for-large-datasets-in-helsinki-79ebc7288c91/) ## [Nearest Neighbor Analysis for Large Datasets in Helsinki Region](https://towardsdatascience.com/nearest-neighbor-analysis-for-large-datasets-in-helsinki-79ebc7288c91/) [Data Science](https://towardsdatascience.com/category/data-science/) BallTree function for efficient distance analysis: Bus stops and restaurants [Bryan Vallejo](https://towardsdatascience.com/author/bryanvallejo16/) December 29, 20217 min read * [![](../images/008.png)](https://towardsdatascience.com/digging-into-my-year-of-spotify-streaming-with-track-embeddings-6cad51523b0e/) ## [Digging Into My Year of Spotify Streaming with Track Embeddings](https://towardsdatascience.com/digging-into-my-year-of-spotify-streaming-with-track-embeddings-6cad51523b0e/) [Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/) I take a high-level look at my year of music streaming [Mads Kalør](https://towardsdatascience.com/author/mkaloer/) January 12, 20229 min read * [![](../images/009.gif)](https://towardsdatascience.com/custom-memory-for-chatgpt-api-artificial-intelligence-python-722d627d4d6d/) ## [Custom Memory for ChatGPT API](https://towardsdatascience.com/custom-memory-for-chatgpt-api-artificial-intelligence-python-722d627d4d6d/) [Artificial Intelligence](https://towardsdatascience.com/category/artificial-intelligence/) A Gentle Introduction to LangChain Memory Types [Andrea Valenzuela](https://towardsdatascience.com/author/andvalenzuela/) August 20, 20239 min read * [![](../images/010.jpeg)](https://towardsdatascience.com/how-to-build-an-impressive-data-science-resume-7a9c71f761c5/) ## [How to Build an Impressive Data Science Resume?](https://towardsdatascience.com/how-to-build-an-impressive-data-science-resume-7a9c71f761c5/) [Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/) Tips to make an impactful resume that stands out [Sharan Kumar Ravindran](https://towardsdatascience.com/author/rsharankumar/) April 17, 20217 min read * [![](../images/011.jpg)](https://towardsdatascience.com/optimising-non-linear-treatment-effects-in-pricing-and-promotions-011ce140d180/) ## [Optimising Non-Linear Treatment Effects in Pricing and Promotions](https://towardsdatascience.com/optimising-non-linear-treatment-effects-in-pricing-and-promotions-011ce140d180/) [Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/) Causal AI, exploring the integration of causal reasoning into machine learning [Ryan OSullivan](https://towardsdatascience.com/author/raz1470/) May 24, 202412 min read * [![](../images/012.jpg)](https://towardsdatascience.com/step-by-step-basics-text-classifier-e666c6bac52b/) ## [Step by Step Basics: Text Classifier](https://towardsdatascience.com/step-by-step-basics-text-classifier-e666c6bac52b/) [NLP](https://towardsdatascience.com/category/artificial-intelligence/nlp/) An Instructional Guide and Flow Diagram for Building a Supervised Machine Learning Text Classifier in Python [Lucy Dickinson](https://towardsdatascience.com/author/lucydickinson/) February 17, 202311 min read * [YouTube](https://www.youtube.com/c/TowardsDataScience) * [X](https://x.com/TDataScience) * [LinkedIn](https://www.linkedin.com/company/towards-data-science/) * [Threads](https://www.threads.net/@towardsdatascience) * [Bluesky](https://bsky.app/profile/towardsdatascience.com) [](https://towardsdatascience.com/) Your home for data science and AI. The world's leading publication for data science, data analytics, data engineering, machine learning, and artificial intelligence professionals. Subscribe to Our Newsletter[Write For TDS](https://towardsdatascience.com/submissions/)•[About](https://towardsdatascience.com/about-towards-data-science-d691af11cc2f/)•[Advertise](https://contact.towardsdatascience.com/advertise-with-towards-data-science)•[Privacy Policy](https://towardsdatascience.com/privacy-policy/)•[Terms of Use](https://towardsdatascience.com/website-terms-of-use/) © Insight Media Group, LLC 2026•[The New Stack](https://thenewstack.io)•[roadmap.sh](https://roadmap.sh)•[Creator Network](https://insightmediagroup.io/creator-network) #### Recommended Articles Close * [ ![](https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607686/image?etag=1782161464448&width=500&height=500) How Relevance Models Foreshadowed Transformers for NLP ](https://towardsdatascience.com/how-relevance-models-foreshadowed-transformers-for-nlp/ "How Relevance Models Foreshadowed Transformers for NLP") * [ ![](https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607639/image?etag=1781250125848&width=500&height=500) Javascript Fatigue: HTMX Is All You Need to Build ChatGPT — Part 1 ](https://towardsdatascience.com/javascript-fatigue-you-dont-need-js-to-build-chatgpt/ "Javascript Fatigue: HTMX Is All You Need to Build ChatGPT — Part 1") * [ ![](https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607930/image?etag=1782124566054&width=500&height=500) The Subset Sum Problem Solved in Linear Time for Dense Enough Inputs ](https://towardsdatascience.com/subset-sum-problem-solved-in-linear-time-for-dense-enough-inputs/ "The Subset Sum Problem Solved in Linear Time for Dense Enough Inputs") * [ ![](https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/3660/image?etag=1780176246070&width=500&height=500) Does Your Company Have a Data Strategy? ](https://towardsdatascience.com/does-your-company-have-a-data-strategy-e8944dbec4ae/ "Does Your Company Have a Data Strategy?")