GET https://rct.dev.bbntimes.com/science/mathematics-of-machine-learning-data-algorithm-model-and-causal-learning

Response
200 OK
IP
3.145.71.171
Profiled on
Token
2ae725

ArticleController :: show

Request

GET Parameters

None

POST Parameters

None

Uploaded Files

None

Request Attributes

Key Value
_controller 
"App\Controller\ArticleController::show"
_firewall_context 
"security.firewall.map.context.main"
_links 
Symfony\Component\WebLink\GenericLinkProvider {#3588
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    3707 => Symfony\Component\WebLink\Link {#3707
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      -attributes: [
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    3706 => Symfony\Component\WebLink\Link {#3706
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      -rel: [
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      -attributes: [
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    3705 => Symfony\Component\WebLink\Link {#3705
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    3703 => Symfony\Component\WebLink\Link {#3703
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      ]
      -attributes: [
        "as" => "script"
      ]
    }
    3702 => Symfony\Component\WebLink\Link {#3702
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      -rel: [
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      ]
      -attributes: [
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      ]
    }
    3701 => Symfony\Component\WebLink\Link {#3701
      -href: "/build/scroll-infinite-article.js"
      -rel: [
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      ]
      -attributes: [
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      ]
    }
    3700 => Symfony\Component\WebLink\Link {#3700
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      -attributes: [
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      ]
    }
    3699 => Symfony\Component\WebLink\Link {#3699
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      -attributes: [
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      ]
    }
    3698 => Symfony\Component\WebLink\Link {#3698
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      -rel: [
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      -attributes: [
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      ]
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    3697 => Symfony\Component\WebLink\Link {#3697
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      -attributes: [
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      ]
    }
    3696 => Symfony\Component\WebLink\Link {#3696
      -href: "/build/comment-css.css"
      -rel: [
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      -attributes: [
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      ]
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}
_route 
"article_show"
_route_params 
[
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]
_security_firewall_run 
"_security_main"
_stopwatch_token 
"b26200"
category 
"science"
slug 
"mathematics-of-machine-learning-data-algorithm-model-and-causal-learning"

Request Headers

Header Value
accept 
"*/*"
accept-encoding 
"gzip, br, zstd, deflate"
connection 
"close"
cookie 
"PHPSESSID=2evtkdv42ntst5f90dl8n601kn"
host 
"rct.dev.bbntimes.com"
user-agent 
"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
x-php-ob-level 
"1"

Request Content

Request content not available (it was retrieved as a resource).

Response

Response Headers

Header Value
cache-control 
"no-cache, private"
content-type 
"text/html; charset=UTF-8"
date 
"Sat, 22 Feb 2025 13:44:43 GMT"
link 
"</build/runtime.js>; rel="preload"; as="script",</build/644.js>; rel="preload"; as="script",</build/502.js>; rel="preload"; as="script",</build/app.js>; rel="preload"; as="script",</build/view-more.js>; rel="preload"; as="script",</build/term-condition.js>; rel="preload"; as="script",</build/contact.js>; rel="preload"; as="script",</build/scroll-infinite-article.js>; rel="preload"; as="script",</build/app.css>; rel="preload"; as="style",</build/cookie-style.css>; rel="preload"; as="style",</build/term-condition-css.css>; rel="preload"; as="style",</build/contact-css.css>; rel="preload"; as="style",</build/comment-css.css>; rel="preload"; as="style""
x-debug-token 
"2ae725"

Cookies

Request Cookies

Key Value
PHPSESSID 
"2evtkdv42ntst5f90dl8n601kn"

Response Cookies

No response cookies

Session 6

Session Metadata

Key Value
Created 
"Sat, 22 Feb 25 13:44:26 +0000"
Last used 
"Sat, 22 Feb 25 13:44:42 +0000"
Lifetime 
0

Session Attributes

Attribute Value
_csrf/https-comment 
"WvYpcok38QwoOh0woNCpi2k8m8o9acyHp6DTIKULm3A"
_csrf/https-cookie_accept 
"epYtzKvSDL8JH0fPqnUR_24cPbeUiLv-iZmC2h0GUJ4"

Session Usage

6 Usages
Stateless check enabled
Usage
Symfony\Component\Security\Csrf\TokenStorage\SessionTokenStorage:76
Show trace 
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Symfony\Component\Security\Csrf\TokenStorage\SessionTokenStorage:79
Show trace 
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Symfony\Component\Security\Csrf\TokenStorage\SessionTokenStorage:52
Show trace 
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Symfony\Component\Security\Csrf\TokenStorage\SessionTokenStorage:56
Show trace 
[
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    "function" => "show"
    "class" => "App\Controller\ArticleController"
    "type" => "->"
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    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 76
    "function" => "handleRaw"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
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  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/Kernel.php"
    "line" => 197
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
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  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/runtime/Runner/Symfony/HttpKernelRunner.php"
    "line" => 35
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\Kernel"
    "type" => "->"
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  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    "line" => 29
    "function" => "run"
    "class" => "Symfony\Component\Runtime\Runner\Symfony\HttpKernelRunner"
    "type" => "->"
  ]
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    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/public/index.php"
    "line" => 5
    "args" => [
      "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    ]
    "function" => "require_once"
  ]
]
Symfony\Component\Security\Core\Authentication\Token\Storage\UsageTrackingTokenStorage:41
Show trace 
[
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/security-core/Authentication/Token/Storage/UsageTrackingTokenStorage.php"
    "line" => 41
    "function" => "getMetadataBag"
    "class" => "Symfony\Component\HttpFoundation\Session\Session"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/twig-bridge/AppVariable.php"
    "line" => 103
    "function" => "getToken"
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    "function" => "twig_get_attribute"
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    "function" => "handle"
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    "function" => "handleRaw"
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    "type" => "->"
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    "function" => "handle"
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    "function" => "run"
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    "args" => [
      "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    ]
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]
Symfony\Component\Security\Http\Firewall\ContextListener:171
Show trace 
[
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/security-http/Firewall/ContextListener.php"
    "line" => 171
    "function" => "remove"
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    "function" => "onKernelResponse"
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    "function" => "__invoke"
    "class" => "Symfony\Component\EventDispatcher\Debug\WrappedListener"
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    "function" => "callListeners"
    "class" => "Symfony\Component\EventDispatcher\EventDispatcher"
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    "function" => "dispatch"
    "class" => "Symfony\Component\EventDispatcher\EventDispatcher"
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    "function" => "filterResponse"
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]

Flashes

Flashes

No flash messages were created.

Server Parameters

Server Parameters

Defined in .env

Key Value
APP_ENV 
"dev"
APP_SECRET 
"0a988e63f011514eaabfc650b599af4d"
CORS_ALLOW_ORIGIN 
"*"
DATABASE_URL 
"mysql://bbndb_rctuser:33F5W25z40or0f7@localhost:3306/rct_bbntimes"
GOOGLE_RECAPTCHA_SECRET_KEY 
"6LdV5fgpAAAAANxzTG8ZMfIjil1wu-1vrQvnUt-x"
GOOGLE_RECAPTCHA_SITE_KEY 
"6LdV5fgpAAAAAENKcn73MJAhQrbtQeqgyC4wDLMP"
MAILER_DSN 
"smtp://no-reply%40rct.dev.bbntimes.com:Bl6%26gLD48%26Of919@rct.dev.bbntimes.com:465"
MARIADB_PASSWORD 
"i!87pK&!85ezc8"

Defined as regular env variables

Key Value
APP_DEBUG 
"1"
BASE 
"/public"
CONTEXT_DOCUMENT_ROOT 
"/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com"
CONTEXT_PREFIX 
""
DOCUMENT_ROOT 
"/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com"
FCGI_ROLE 
"RESPONDER"
GATEWAY_INTERFACE 
"CGI/1.1"
HTTPS 
"on"
HTTP_ACCEPT 
"*/*"
HTTP_ACCEPT_ENCODING 
"gzip, br, zstd, deflate"
HTTP_CONNECTION 
"close"
HTTP_COOKIE 
"PHPSESSID=2evtkdv42ntst5f90dl8n601kn"
HTTP_HOST 
"rct.dev.bbntimes.com"
HTTP_USER_AGENT 
"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
PASSENGER_COMPILE_NATIVE_SUPPORT_BINARY 
"0"
PASSENGER_DOWNLOAD_NATIVE_SUPPORT_BINARY 
"0"
PATH 
"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/snap/bin"
PHP_SELF 
"/public/index.php"
PP_CUSTOM_PHP_CGI_INDEX 
"plesk-php81-fastcgi"
PP_CUSTOM_PHP_INI 
"/var/www/vhosts/system/rct.dev.bbntimes.com/etc/php.ini"
QUERY_STRING 
""
REDIRECT_BASE 
"/public"
REDIRECT_HTTPS 
"on"
REDIRECT_PASSENGER_COMPILE_NATIVE_SUPPORT_BINARY 
"0"
REDIRECT_PASSENGER_DOWNLOAD_NATIVE_SUPPORT_BINARY 
"0"
REDIRECT_REDIRECT_HTTPS 
"on"
REDIRECT_REDIRECT_PASSENGER_COMPILE_NATIVE_SUPPORT_BINARY 
"0"
REDIRECT_REDIRECT_PASSENGER_DOWNLOAD_NATIVE_SUPPORT_BINARY 
"0"
REDIRECT_REDIRECT_SCRIPT_URI 
"https://rct.dev.bbntimes.com/science/mathematics-of-machine-learning-data-algorithm-model-and-causal-learning"
REDIRECT_REDIRECT_SCRIPT_URL 
"/science/mathematics-of-machine-learning-data-algorithm-model-and-causal-learning"
REDIRECT_REDIRECT_SSL_TLS_SNI 
"rct.dev.bbntimes.com"
REDIRECT_REDIRECT_STATUS 
"200"
REDIRECT_REDIRECT_UNIQUE_ID 
"Z7nUypDyWLT8YV1VjBpaxgAAAIM"
REDIRECT_SCRIPT_URI 
"https://rct.dev.bbntimes.com/science/mathematics-of-machine-learning-data-algorithm-model-and-causal-learning"
REDIRECT_SCRIPT_URL 
"/science/mathematics-of-machine-learning-data-algorithm-model-and-causal-learning"
REDIRECT_SSL_TLS_SNI 
"rct.dev.bbntimes.com"
REDIRECT_STATUS 
"200"
REDIRECT_UNIQUE_ID 
"Z7nUypDyWLT8YV1VjBpaxgAAAIM"
REDIRECT_URL 
"/public/science/mathematics-of-machine-learning-data-algorithm-model-and-causal-learning"
REMOTE_ADDR 
"3.145.71.171"
REMOTE_PORT 
"37416"
REQUEST_METHOD 
"GET"
REQUEST_SCHEME 
"https"
REQUEST_TIME 
1740231882
REQUEST_TIME_FLOAT 
1740231882.9797
REQUEST_URI 
"/science/mathematics-of-machine-learning-data-algorithm-model-and-causal-learning"
SCRIPT_FILENAME 
"/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/public/index.php"
SCRIPT_NAME 
"/public/index.php"
SCRIPT_URI 
"https://rct.dev.bbntimes.com/science/mathematics-of-machine-learning-data-algorithm-model-and-causal-learning"
SCRIPT_URL 
"/science/mathematics-of-machine-learning-data-algorithm-model-and-causal-learning"
SERVER_ADDR 
"5.196.1.209"
SERVER_ADMIN 
"[no address given]"
SERVER_NAME 
"rct.dev.bbntimes.com"
SERVER_PORT 
"443"
SERVER_PROTOCOL 
"HTTP/1.1"
SERVER_SIGNATURE 
"<address>Apache Server at rct.dev.bbntimes.com Port 443</address>\n"
SERVER_SOFTWARE 
"Apache"
SSL_TLS_SNI 
"rct.dev.bbntimes.com"
SYMFONY_DOTENV_VARS 
"APP_ENV,APP_SECRET,DATABASE_URL,MARIADB_PASSWORD,CORS_ALLOW_ORIGIN,MAILER_DSN,GOOGLE_RECAPTCHA_SECRET_KEY,GOOGLE_RECAPTCHA_SITE_KEY"
UNIQUE_ID 
"Z7nUypDyWLT8YV1VjBpaxgAAAIM"

Sub Requests 6

CookieController :: renderAnalysis (token = b60744)

Key Value
_controller 
"App\Controller\CookieController::renderAnalysis"
_format 
"html"
_locale 
"en"
_stopwatch_token 
"64d7cd"

AppController :: renderHeader (token = 26a0fb)

Key Value
_controller 
"App\Controller\AppController::renderHeader"
_format 
"html"
_locale 
"en"
_stopwatch_token 
"5573af"
slug 
"home"

ArticleController :: trendingArticle (token = d1f558)

Key Value
_controller 
"App\Controller\ArticleController::trendingArticle"
_format 
"html"
_locale 
"en"
_stopwatch_token 
"e57924"
category 
"Science"

ArticleController :: relatedArticles (token = beca47)

Key Value
_controller 
"App\Controller\ArticleController::relatedArticles"
_format 
"html"
_locale 
"en"
_stopwatch_token 
"fb8400"
current_article 
App\Entity\Article {#1094
  -id: 9225
  -title: "Mathematics of Machine Learning: Data, Algorithm, Model, and Causal Learning"
  -slug: "mathematics-of-machine-learning-data-algorithm-model-and-causal-learning"
  -introtext: "<p>There are 4 concepts that are at the core of <a href="technology/machine-learning-a-beginners-guide-and-why-is-it-important-for-your-business" target="_blank" rel="noopener">machine learning</a> (ML): data, algorithm, a model, and statistical learning.</p>\r\n"
  -content: """
    \r\n
    <p><a href="technology/this-is-how-machine-learning-can-drive-space-exploration" target="_blank" rel="noopener">Machine learning</a> is about designing algorithms that automatically extract valuable information from statistical data. The emphasis here is on correlations and “automatism”, i.e., machine learning is concerned about general-purpose methodologies that can be applied to many datasets, while producing something that is meaningful.</p>\r\n
    <p>Since machine learning is inherently data driven, data is at the core data of machine learning. The goal of machine learning is to design general-purpose methodologies to extract valuable patterns from data, ideally without much domain-specific expertise.</p>\r\n
    <p>A “machine learning algorithm” means a system that makes predictions based on input data, named as predictors. Or, the “machine learning algorithm” means a system that adapts some internal parameters of the predictor to perform well on future unseen input data.</p>\r\n
    <p>A model is said to learn from data if its performance on a given task improves after the data is taken into account. The goal is to find good models that generalize well to yet unseen data, which we may care about in the future.</p>\r\n
    <p>Learning can be understood as a learning way to automatically find patterns and structure in data by optimizing the parameters of the model.</p>\r\n
    <h2>Mathematics for Machine Learning</h2>\r\n
    <p>Statistical Machine Learning involves mathematical fields, such as linear algebra, function analysis, or calculus, geometry, discrete mathematics, statistics, probability theory and mathematical programming.</p>\r\n
    <p>But such a <a href="technology/the-difference-between-machine-learning-and-deep-learning" target="_blank" rel="noopener">machine learning </a>is missing the fundamentals of dataset theory, a foundational system for the whole of mathematics, as well as computer science and <a href="technology/artificial-intelligence-machine-learning-and-the-future-of-graphs" target="_blank" rel="noopener">data-driven AI</a>.</p>\r\n
    <h2><strong>The Set Theory for Machine Learning</strong></h2>\r\n
    <p>An AI dataset is not a set or multiset, list, bunch, bag, heap, sample, weighted set, collection, and suite, but a poset.</p>\r\n
    <p>A set is merely gathering together into a whole of definite, distinct, well-defined objects, the set's elements or members, as data, numbers, people, letters of the alphabet, other sets, and so on.</p>\r\n
    <p>Machine data/representation/concept/category learning/formation is the machine learning task of learning a function that maps an input to an output based on example input-output pairs, as the feature vector space X and its label space Y. And a learning algorithm seeks a function f, where X is the input space and Y is the output space, of some space of possible functions F, called the&nbsp;hypothesis space.</p>\r\n
    <p>It infers a function from labeled training data consisting of a set of training examples, where each example is a pair consisting of an input object (typically a vector) and a desired output value (also called the supervisory signal). A supervised learning algorithm analyzes the training data and produces an inferred function, which can be used for mapping new examples. An optimal scenario will allow for the algorithm to correctly determine the class labels for unseen instances. This requires the learning algorithm to generalize from the training data to unseen situations in a "reasonable" way.</p>\r\n
    <p>A partially ordered set (poset) formalizes and generalizes the concept of an ordering, sequencing, or arrangement of the elements of a set.</p>\r\n
    <p>Formally, a partial order is any binary relation that is reflexive, antisymmetric, and transitive.</p>\r\n
    <p>A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering. Again, there may be pairs of elements for which neither element precedes the other in the poset. Partial orders thus generalize total orders, in which every pair is comparable.</p>\r\n
    <p>A poset can be visualized through its Hasse diagram, which depicts the ordering relation.</p>\r\n
    <div class="gmail-slate-resizable-image-embed gmail-slate-image-embed__resize-full-width"><img src="/images/Hasse_Diagram.png" alt="Hasse_Diagram.png" /></div>\r\n
    <p>The Hasse diagram of the set of all subsets of a three-element set {x, y, z}, ordered by inclusion.</p>\r\n
    <p>Standard examples of data posets include:</p>\r\n
    <ul>\r\n
    <li>The real numbers ordered by the standard less-than-or-equal relation ≤ (a totally ordered set as well).</li>\r\n
    <li>The set of subsets of a given set (its power set) ordered by inclusion.</li>\r\n
    <li>The set of sequences ordered by subsequence, and the set of strings ordered by substring.</li>\r\n
    <li>The set of natural numbers equipped with the relation of divisibility.</li>\r\n
    <li>The vertex set of a directed acyclic graph ordered by reachability.</li>\r\n
    <li>The set of subspaces of a vector space ordered by inclusion.</li>\r\n
    <li>The set of events in special relativity and general relativity, where for two events X and Y, X ≤ Y if and only if Y is in the future light cone of X. An event Y can only be causally affected by X if X ≤ Y.</li>\r\n
    <li>A collection of people ordered by genealogical descendancy. Some pairs of people bear the descendant-ancestor relationship, but other pairs of people are incomparable, with neither being a descendant of the other.</li>\r\n
    </ul>\r\n
    <p>Now, a data set (or dataset) is defined as a collection of data, listing values for each of the variables for each member of the data set. In the case of tabular data, a data set corresponds to database tables, where every column represents a particular variable or feature and attribute, and each row corresponds to a given record of the data set in question.</p>\r\n
    <p>But data sets can also consist of a collection of documents or files. Data set is the unit to measure the information released in a public open data repository. The European Open Data portal mentions &gt; half a million data sets.</p>\r\n
    <p>So, no consensus about it, if not take a data poset as the common background.</p>\r\n
    <h2>Conclusion</h2>\r\n
    <p>Overall, there are two generations of machine learning: statistical machine learning (SML) and&nbsp;causal machine learning (CML).</p>\r\n
    <p>There are 5 concepts behind causal machine learning: reality, data, causal algorithm, a causal model, and causal learning.</p>\r\n
    <p><a href="https://www.barnesandnoble.com/w/science-and-technology-21-new-physica-azamat-abdoullaev/1124928170" target="_blank" rel="noopener"><img src="/images/Science_and_Technology_New_Physica.jpeg" alt="Science_and_Technology_New_Physica.jpeg" /></a></p>\r\n
    <p><em>Science and Technology 21, New Physica by&nbsp;Azamat Abdoullaev</em> - Read the e-book version <a href="https://www.barnesandnoble.com/w/science-and-technology-21-new-physica-azamat-abdoullaev/1124928170" target="_blank" rel="noopener">here</a>.&nbsp;</p>
    """
  -user: Proxies\__CG__\App\Entity\User {#1092 …}
  -createdAt: DateTime @1627895872 {#1145
    date: 2021-08-02 09:17:52.0 UTC (+00:00)
  }
  -updatedAt: DateTime @1627899237 {#1150
    date: 2021-08-02 10:13:57.0 UTC (+00:00)
  }
  -deletedAt: null
  -category: App\Entity\Category {#445 …}
  -status: "published"
  -imageCard: Proxies\__CG__\App\Entity\File {#1184 …}
  -ImageHeader: Proxies\__CG__\App\Entity\File {#1184 …}
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  -clicks: 3610
  -comments: Doctrine\ORM\PersistentCollection {#1125 …}
  -reviewed_at: DateTime @1627895872 {#1148
    date: 2021-08-02 09:17:52.0 UTC (+00:00)
  }
  -metakey: "Mathematics of Machine Learning: Data, Algorithm, Model, and Causal Learning"
  -metadesc: "There are 4 concepts that are at the core of machine learning (ML): data, algorithm, a model, and statistical learning."
  -robots: null
  -publishedAt: DateTime @1627895872 {#1147
    date: 2021-08-02 09:17:52.0 UTC (+00:00)
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  -canonical: null
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}

AppController :: renderFooter (token = cc0dcf)

Key Value
_controller 
"App\Controller\AppController::renderFooter"
_format 
"html"
_locale 
"en"
_stopwatch_token 
"54b339"

CookieController :: renderCookie (token = a23d12)

Key Value
_controller 
"App\Controller\CookieController::renderCookie"
_format 
"html"
_locale 
"en"
_stopwatch_token 
"ae0e49"