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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Predictive learning</span></span>

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<p><b>Predictive learning</b> is a <a href="Machine_learning" title="Machine learning">machine learning</a> (ML) technique where an <a href="Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a> model is fed new data to develop an understanding of its environment, capabilities, and limitations. This technique finds application in many areas, including <a href="Neuroscience" title="Neuroscience">neuroscience</a>, <a href="Business" title="Business">business</a>, <a href="Robotics" title="Robotics">robotics</a>, and <a href="Computer_vision" title="Computer vision">computer vision</a>. This concept was developed and expanded by French computer scientist <a href="Yann_LeCun" title="Yann LeCun">Yann LeCun</a> in 1988 during his career at <a href="Bell_Labs" title="Bell Labs">Bell Labs</a>, where he trained models to detect handwriting so that financial companies could automate check processing.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>The mathematical foundation for predictive learning dates back to the 17th century, where British insurance company <a href="Lloyd's_of_London" title="Lloyd's of London">Lloyd's</a> used <a href="Predictive_analytics" title="Predictive analytics">predictive analytics</a> to make a profit.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Starting out as a mathematical concept, this method expanded the possibilities of artificial intelligence. Predictive learning is an attempt to learn with a minimum of pre-existing mental structure. It was inspired by <a href="Jean_Piaget" title="Jean Piaget">Jean Piaget</a>'s account of children <a href="Reinforcement_learning" title="Reinforcement learning">constructing knowledge of the world through interaction</a>. <a href="Gary_Drescher" title="Gary Drescher">Gary Drescher</a>'s book <i>Made-up Minds</i> was crucial to the development of this concept.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>The idea that predictions and <a href="Unconscious_inference" title="Unconscious inference">unconscious inference</a> are used by the brain to construct a model of the world, in which it can identify causes of <a href="Percepts" class="mw-redirect" title="Percepts">percepts</a>, goes back even further to <a href="Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a>'s iteration of this study. These ideas were further developed by the field of <a href="Predictive_coding" title="Predictive coding">predictive coding</a>. Another related predictive learning theory is <a href="Jeff_Hawkins" title="Jeff Hawkins">Jeff Hawkins</a>' <a href="Memory-prediction_framework" title="Memory-prediction framework">memory-prediction framework</a>, which is laid out in his book <i><a href="On_Intelligence" title="On Intelligence">On Intelligence</a></i>.

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<div class="mw-heading mw-heading2"><h2 id="Mathematical_procedures">Mathematical procedures</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Training_process">Training process</h3></div>

<p>Similar to ML, predictive learning aims to extrapolate the value of an unknown dependent variable <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}">

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<annotation encoding="application/x-tex">{\displaystyle Y}</annotation>

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</math></span><img src="./961d67d6b454b4df2301ac571808a3538b3a6d3f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}" loading="lazy"></span>, given independent input data <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X=(x_{1},x_{2},\dots ,x_{n})}">

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<annotation encoding="application/x-tex">{\displaystyle X=(x_{1},x_{2},\dots ,x_{n})}</annotation>

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</math></span><img src="./d0d6fc20f2ecc9bac5c4d7aa8571594dbe673f76.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.416ex; height:2.843ex;" alt="{\displaystyle X=(x_{1},x_{2},\dots ,x_{n})}" loading="lazy"></span>. A set of attributes can be classified into <a href="Categorical_variable" title="Categorical variable">categorical</a> data (discrete factors such as race, sex, or affiliation) or numerical data (continuous values such as temperature, annual income, or speed). Every set of input values is fed into a <a href="Neural_network_(machine_learning)" title="Neural network (machine learning)">neural network</a> to predict a value <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}">

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<annotation encoding="application/x-tex">{\displaystyle y}</annotation>

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</math></span><img src="./b8a6208ec717213d4317e666f1ae872e00620a0d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}" loading="lazy"></span>. In order to predict the output accurately, the <a href="Weighting" class="mw-redirect" title="Weighting">weights</a> of the neural network (which represent how much each predictor variable affects the outcome) must be incrementally adjusted via <a href="Backpropagation" title="Backpropagation">backpropagation</a> to produce estimates closer to the actual data.

</p><p>Once an ML model is given enough adjustments through training to predict values closer to the <a href="Ground_truth" title="Ground truth">ground truth</a>, it should be able to correctly predict outputs of new data with little <a href="Errors_and_residuals" title="Errors and residuals">error</a>.

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<div class="mw-heading mw-heading3"><h3 id="Maximizing_accuracy">Maximizing accuracy</h3></div>

<p>In order to ensure maximum accuracy for a predictive learning model, the predicted values <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {y}}=F(x)}">

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<annotation encoding="application/x-tex">{\displaystyle {\hat {y}}=F(x)}</annotation>

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</math></span><img src="./ad1ceaa8141c3c194c685cac4d222e286d88e1e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.28ex; height:2.843ex;" alt="{\displaystyle {\hat {y}}=F(x)}" loading="lazy"></span> must not exceed a certain error threshold when compared to actual values <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}">

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<annotation encoding="application/x-tex">{\displaystyle y}</annotation>

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</math></span><img src="./b8a6208ec717213d4317e666f1ae872e00620a0d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}" loading="lazy"></span> by the risk formula:

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<annotation encoding="application/x-tex">{\displaystyle R(F)=E_{xy}L(y,F(x))}</annotation>

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</math></span><img src="./0e420f2431200bfeffc0e515154e0600c9e77bd9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:22.579ex; height:3.009ex;" alt="{\displaystyle R(F)=E_{xy}L(y,F(x))}" loading="lazy"></span>,</dd></dl>

<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L}">

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<annotation encoding="application/x-tex">{\displaystyle L}</annotation>

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</math></span><img src="./103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}" loading="lazy"></span> is the <a href="Loss_function" title="Loss function">loss function</a>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}">

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<annotation encoding="application/x-tex">{\displaystyle y}</annotation>

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</math></span><img src="./b8a6208ec717213d4317e666f1ae872e00620a0d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}" loading="lazy"></span> is the ground truth, and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(x)}">

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<annotation encoding="application/x-tex">{\displaystyle F(x)}</annotation>

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</math></span><img src="./71a82805d469cdfa7856c11d6ee756acd1dc7174.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.88ex; height:2.843ex;" alt="{\displaystyle F(x)}" loading="lazy"></span> is the predicted data. This error function is used to make incremental adjustments to the model's weights to eventually reach a well-trained prediction of:<sup id="cite_ref-:1_4-0" class="reference"><a href="#cite_note-:1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

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<annotation encoding="application/x-tex">{\displaystyle F^{*}(x)={\underset {F(x)}{\operatorname {argmin} }}\,E_{xy}}</annotation>

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</math></span><img src="./be3c7961a1e942c5e70a2dd5578e4edcafcdd5c1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:20.31ex; height:5.009ex;" alt="{\displaystyle F^{*}(x)={\underset {F(x)}{\operatorname {argmin} }}\,E_{xy}}" loading="lazy"></span><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L(y,F(x))}">

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<annotation encoding="application/x-tex">{\displaystyle L(y,F(x))}</annotation>

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</math></span><img src="./7da73aa7583b8fa4bb3729fbe01cbf42a5eacb8d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.461ex; height:2.843ex;" alt="{\displaystyle L(y,F(x))}" loading="lazy"></span></dd></dl>

<p>Once the error is negligible or considered small enough after training, the model is said to have <a href="Convergence_(logic)" title="Convergence (logic)">converged</a>.

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<div class="mw-heading mw-heading3"><h3 id="Ensemble_learning">Ensemble learning</h3></div>

<p>In some cases, using a singular machine learning approach is not enough to create an accurate estimate for certain data. <a href="Ensemble_learning" title="Ensemble learning">Ensemble learning</a> is the combination of several ML algorithms to create a stronger model. Each model is represented by the function

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<annotation encoding="application/x-tex">{\displaystyle F(x)=a_{0}+\sum _{m=1}^{M}a_{m}f_{m}(x)}</annotation>

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</math></span><img src="./bd565d8e57da8aaa89b75793dc893b542f65e98b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:25.891ex; height:7.343ex;" alt="{\displaystyle F(x)=a_{0}+\sum _{m=1}^{M}a_{m}f_{m}(x)}" loading="lazy"></span>,</dd></dl>

<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}">

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<annotation encoding="application/x-tex">{\displaystyle M}</annotation>

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</math></span><img src="./f82cade9898ced02fdd08712e5f0c0151758a0dd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}" loading="lazy"></span> is the number of ensemble models, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{0}}">

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<annotation encoding="application/x-tex">{\displaystyle a_{0}}</annotation>

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</math></span><img src="./693ad9f934775838bd72406b41ada4a59785d7ba.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.009ex;" alt="{\displaystyle a_{0}}" loading="lazy"></span> is the bias, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{m}}">

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<annotation encoding="application/x-tex">{\displaystyle a_{m}}</annotation>

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</math></span><img src="./e579a0eee7d28a69a7e8b666784aeed3baa8d617.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.905ex; height:2.009ex;" alt="{\displaystyle a_{m}}" loading="lazy"></span> is the weight corresponding to each <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}">

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<annotation encoding="application/x-tex">{\displaystyle m}</annotation>

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</math></span><img src="./0a07d98bb302f3856cbabc47b2b9016692e3f7bc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}" loading="lazy"></span>-th variable, and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{m}(x)}">

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</math></span><img src="./9a6fbf7d6f84750af92ff5060f6f23133909975a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.953ex; height:2.843ex;" alt="{\displaystyle f_{m}(x)}" loading="lazy"></span> is the <a href="Activation_function" title="Activation function">activation function</a> corresponding to each variable. An ensemble learning model is represented as a <a href="Linear_combination" title="Linear combination">linear combination</a> of the predictions from each constituent approach,

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<annotation encoding="application/x-tex">{\displaystyle {\hat {a}}_{m}={\underset {a_{m}}{\operatorname {argmin} }}\sum _{i=1}^{N}L\left(y_{i},a_{0}+\sum _{m=1}^{M}a_{m}f_{m}(x_{i})\right)+\lambda \sum _{m=1}^{M}|a_{m}|}</annotation>

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</math></span><img src="./6ae1973bd28a9d3a04e354a1c202f5638ca48e2c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:57.293ex; height:7.509ex;" alt="{\displaystyle {\hat {a}}_{m}={\underset {a_{m}}{\operatorname {argmin} }}\sum _{i=1}^{N}L\left(y_{i},a_{0}+\sum _{m=1}^{M}a_{m}f_{m}(x_{i})\right)+\lambda \sum _{m=1}^{M}|a_{m}|}" loading="lazy"></span></dd></dl>

<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y_{i}}">

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</math></span><img src="./67d30d30b6c2dbe4d6f150d699de040937ecc95f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.939ex; height:2.009ex;" alt="{\displaystyle y_{i}}" loading="lazy"></span> is the actual value, the second parameter is the value predicted by each constituent method, and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }">

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</math></span><img src="./b43d0ea3c9c025af1be9128e62a18fa74bedda2a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }" loading="lazy"></span> is a coefficient representing each model's variation for a certain predictor variable.<sup id="cite_ref-:1_4-1" class="reference"><a href="#cite_note-:1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Cognitive_development">Cognitive development</h3></div>

<p>Sensorimotor signals are neural impulses sent to the brain upon physical touch. Using predictive learning to detect sensorimotor signals plays a key role in early <a href="Cognitive_development" title="Cognitive development">cognitive development</a>, as the human brain represents sensorimotor signals in a predictive manner (it attempts to minimize prediction error between incoming <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/books/NBK547656/#:~:text=General%20senses%20include%20touch%2C%20pain,utilized%20in%20processing%20general%20senses.">sensory signals</a> and <a rel="nofollow" class="external text" href="https://www.frontiersin.org/articles/10.3389/fpsyg.2013.00276">top–down prediction</a>). In order to update an unadjusted predictor, it must be trained through sensorimotor experiences because it does not inherently have prediction ability.<sup id="cite_ref-:0_5-0" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In a recent research paper, Dr. Yukie Nagai suggested a <a rel="nofollow" class="external text" href="https://royalsocietypublishing.org/doi/10.1098/rstb.2018.0030">new architecture</a> in predictive learning to predict sensorimotor signals based on a two-module approach: a sensorimotor system which interacts with the environment and a predictor which simulates the sensorimotor system in the brain.<sup id="cite_ref-:0_5-1" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading3"><h3 id="Spatiotemporal_memory">Spatiotemporal memory</h3></div>

<p>Computers use predictive learning in spatiotemporal memory to completely create an image given constituent <a href="Frames_(artificial_ingellience)" class="mw-redirect" title="Frames (artificial ingellience)">frames</a>. This implementation uses predictive <a href="Recurrent_neural_network" title="Recurrent neural network">recurrent neural networks</a>, which are neural networks designed to work with sequential data, such as a <a href="Time_series" title="Time series">time series</a>. Using predictive learning in conjunction with computer vision enables computers to create images of their own, which can be helpful when replicating sequential phenomena such as replicating DNA strands, face recognition, or even creating X-ray images.

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<div class="mw-heading mw-heading3"><h3 id="Social_media_consumer_behavior">Social media consumer behavior</h3></div>

<p>In a recent study, data on consumer behavior was collected from various social media platforms such as Facebook, Twitter, LinkedIn, YouTube, Instagram, and Pinterest. The usage of predictive learning analytics led researchers to discover various trends in consumer behavior, such as determining how successful a campaign could be, estimating a fair price for a product to attract consumers, assessing how secure data is, and analyzing the specific audience of the consumers they could target for specific products.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

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<ul><li><a href="Reinforcement_learning" title="Reinforcement learning">Reinforcement learning</a></li>

<li><a href="Predictive_coding" title="Predictive coding">Predictive coding</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.bell-labs.com/institute/blog/yann-lecun-predictive-learning-next-frontier-ai-february-17-2017/">"Yann LeCun "Predictive Learning: The Next Frontier in AI""</a>. <i>Nokia Bell Labs</i>. 2017-02-17<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-11-04</span></span>.</cite></span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFCorporation2019" class="citation web cs1">Corporation, Predictive Success (2019-05-06). <a rel="nofollow" class="external text" href="https://medium.com/@predictivesuccess/a-brief-history-of-predictive-analytics-f05a9e55145f">"A Brief History of Predictive Analytics"</a>. <i>Medium</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-10-27</span></span>.</cite></span>

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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFDrescher1991" class="citation book cs1">Drescher, Gary L. (1991). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=jYsEzeKHLNUC"><i>Made-up Minds: A Constructivist Approach to Artificial Intelligence</i></a>. MIT Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-262-04120-1</bdi>.</cite></span>

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<li id="cite_note-:1-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFFriedmanPopescu2008" class="citation journal cs1">Friedman, Jerome H.; Popescu, Bogdan E. (2008-09-17). <a rel="nofollow" class="external text" href="https://doi.org/10.1214%2F07-AOAS148">"Predictive learning via rule ensembles"</a>. <i>The Annals of Applied Statistics</i>. <b>2</b> (3): <span class="nowrap">916–</span>954. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0811.1679">0811.1679</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1214%2F07-AOAS148">10.1214/07-AOAS148</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1932-6157">1932-6157</a>.</cite></span>

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<li id="cite_note-:0-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFNagai2019" class="citation journal cs1">Nagai, Yukie (2019-04-29). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6452246">"Predictive learning: its key role in early cognitive development"</a>. <i>Philosophical Transactions of the Royal Society B: Biological Sciences</i>. <b>374</b> (1771): 20180030. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frstb.2018.0030">10.1098/rstb.2018.0030</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0962-8436">0962-8436</a>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6452246">6452246</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/30852990">30852990</a>.</cite></span>

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<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFChaudharyAlamAl-RakhamiGumaei2021" class="citation journal cs1">Chaudhary, Kiran; Alam, Mansaf; Al-Rakhami, Mabrook S.; Gumaei, Abdu (2021-05-25). <a rel="nofollow" class="external text" href="https://doi.org/10.1186%2Fs40537-021-00466-2">"Machine learning-based mathematical modelling for prediction of social media consumer behavior using big data analytics"</a>. <i><a href="Journal_of_Big_Data" title="Journal of Big Data">Journal of Big Data</a></i>. <b>8</b> (1): 73. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1186%2Fs40537-021-00466-2">10.1186/s40537-021-00466-2</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2196-1115">2196-1115</a>.</cite></span>

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