NLP research notes
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Q: What is the difference between equation, model, and formula?
An equation usually is a mathematical BALANCE of two operations that are equal. Here are two straightforward examples:
(1) y = 30 - 10 t [this is a math equation with a straight line as its graph]
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(2) y = 3 t^3 - 7 (t) (x) + 8 x^3
When an equation REPRESENTS a specific PHYSICAL event, then the equation would become a formula. For instance, #1 above MAY be a FORMULA in the case of uniformly accelerated motion.
Let (y = Velocity at time t);
let (30 represent the INITIAL velocity)
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let (acceleration be NEGATIVE 10, such as due to gravity).
We can rewrite the equation as a FORMULA: V (t) = V (i) - g t.
Here is another example: I am sure you have learned of the QUADRATIC equation: y = (a x^2) + (b x) + c. Now this is a math equation with a parabola as its graph. We can rewrite this EQUATION and get a FORMULA for a DISTANCE covered by the object in the first example:
s (displacement) = - 5 t^2 + 30 t + 5.
Not ALL equations can be eligible for becoming a formula. Some do.
Some equations MAY represent a SINGULAR event but would NOT be a formula because the event is a special case and not empirical. For example; the following equation: x = 3 t^3 - 2 t^2 + t - 5 may represent the motion of a particle at time t, but it would NOT be an formula of motion for all particles.
Now let’s see what a MODEL is: when architects design a building, they usually construct a MODEL that is to scale of the actual design. This is true for “normal” observable events in our world. But for events that are not readily observable, a MODEL is used to describe how the scientists are imagining/considering the events. In the Newtonian Model, a FORCE is a VECTOR and an UNBALANCED force causes an acceleration. In Bohr’s Model, energy and locales are QUANTIZED. In the wave-particle duality model, light may be a particle or a wave; in Einstein’s Model, the Universe is WARPED (curved).
Bonus: when a new model is accepted by the science world, it has to CORRESPOND to a previously accepted model.
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Source:
https://www.quora.com/What-is-the-difference-between-equation-model-and-formula
Q: What is the difference between a model and an equation?
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An equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. The value(s) of the variable(s) (or unknown(s)) which satisfy the equality is/are called the solution(s) of the equation.
for e.g.
x^2 -5x + 6 = 0 is an equation. In fact it is a quadratic (order 2) equation in one variable (x) and the solutions (roots) of this equation are x= 2 and x =3
<Mathematical model - Wikipedia>
A model is a description of a system using mathematical concepts and language. A model may help to explain a system and to study the effects of different components, and to make predictions about the behaviour of a system in some circumstance. The process developing a model is termed as modelling. A model can take many forms such as statistical models, game theoretic models etc. but in general, mathematical models may include logical models. In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed.
The traditional models include four major elements
Governing Equations: describe how the values of the unknown (dependent) variables will change w.r.t independent variables for e.g. v = (d/dt)s so velocity is a derivative of displacement w.r.t. time. where v-> velocity, s-> displacement, t->time
Defining Equations: They define new quantities in terms of base quantities for e.g. Red, Blue and Green are defined as primary colors and all other colors may be created taking a certain combination of these three colors
Constitutive Equations: They define relation amongst two physical quantities that is specific to a material or substance for e.g. response of a crystal to an electric field, flow of liquid in a pipe etc.
Constraints: They are the set of one or more predefined conditions which the solution must satisfy
So models are usually composed of relationships (operators - algebraic, functions, differential etc.) and variables (abstractions of system parameters of interest that can be quantified).
There could be various types of models according to their structure such as
Linear vs. nonlinear models
Static vs. dynamic models
Explicit vs. implicit models
Discrete vs. continuous models
Deterministic vs. probabilistic models
Deductive, inductive, or floating models
Physical theories are almost invariably expressed using models.
for e.g. Newtonian laws accurately describe many everyday phenomena, but at certain limits relativity theory and quantum mechanics must be used and even these do not apply to all situations and need further refinement. It is possible to obtain the less accurate models in appropriate limits, for example relativistic mechanics reduces to Newtonian mechanics at speeds much less than the speed of light. Quantum mechanics reduces to classical physics when the quantum numbers are high.
It is common to use idealized models in physics to simplify things. Massless ropes, point particles, ideal gases etc. are among the many simplified models used in physics.
The laws of physics are represented with simple equations such as Newton's laws, Maxwell’s equation and Schrodinger equation. These laws are such as a basis for making mathematical models of real situations. Many real situations are very complex and thus modeled approximate on a computer, a model that is computationally feasible to compute is made from the basic laws or from approximate models made from the basic laws. In many other domains like data science models are built based on some assumptions to predict consumer behaviour etc. Since prehistoric times simple models such as maps and diagrams have been used. Often when engineers analyze a system to be controlled or optimized, they use a mathematical model. In analysis, engineers can build a descriptive model of the system as a hypothesis of how the system could work, or try to estimate how an unforeseeable event could affect the system. Similarly, in control of a system, engineers can try out different control approaches in simulations.
To sum up one may say that a model usually describes a system by a set of variables and a set of equations that establish relationships between the variables. The variables represent some properties of the system, for example, measured system outputs often in the form of signals, timing data, counters, and event occurrence (yes/no).
The actual model is the set of functions that describe the relations between the different variables.
Models can be of various types depending on what they are supposed to do for e.g. Predictive Models, Optimization Models etc.
Model building involves the following primary steps:
Training the model or building the model
Testing the model or Model Evaluation
The complexity of a model may vary from model to model and most of the times there is a trade-off between the accuracy of a model and it’s simplicity.
Some models are explicable others could be a black box. They usually perform with a certain level of accuracy , at times within a specified confidence interval, within the scope (predefined criteria) of that model.
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Source:
https://www.quora.com/What-is-the-difference-between-a-model-and-an-equation
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What is meant by back propagation?
Backpropagation is an algorithm used in artificial intelligence (AI) to fine-tune mathematical weight functions and improve the accuracy of an artificial neural network's outputs. ... Backpropagation calculates the mathematical gradient of a loss function with respect to the other weights in the neural network.
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Backpropagation is an algorithm used in artificial intelligence (AI) to fine-tune mathematical weight functions and improve the accuracy of an artificial neural network's outputs.
A neural network can be thought of as a group of connected input/output (I/O) nodes. The level of accuracy each node produces is expressed as a loss function (error rate). Backpropagation calculates the mathematical gradient of a loss function with respect to the other weights in the neural network. The calculations are then used to give artificial network nodes with high error rates less weight than nodes with lower error rates.
Backpropagation uses a methodology called chain rule to improve outputs. Basically, after each forward pass through a network, the algorithm performs a backward pass to adjust the model’s weights.
An important goal of backpropagation is to give data scientists insight into how changing a weight function will change loss functions and the overall behaviour of the neural network. The term is sometimes used as a synonym for "error correction."
Backpropagation as a technique uses gradient descent: It calculates the gradient of the loss function at output, and distributes it back through the layers of a deep neural network. The result is adjusted weights for neurons.
After the emergence of simple feedforward neural networks, where data only goes one way, engineers found that they could use backpropagation to adjust neural input weights after the fact. Backpropagation can be thought of as a way to train a system based on its activity, to adjust how accurately or precisely the neural network processes certain inputs, or how it leads toward some other desired state.
Although backpropagation can be used in both supervised and unsupervised learning, it is usually characterized as being a supervised learning algorithm because in order to calculate a loss function gradient, there must initially be a known, desired output for each input value.
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An approach is a collection of one or more methods to solve a problem.
A method is a collection of one or more algorithms to accomplish a task.
An algorithm is a step-by-step processes to get the desired output.
A model is a mathematical representation of the problem on which the algorithms are applied.
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A model is the presentation in schematic form, often in a simplified way, of an existing or future state or situation. The modelling technique determines the way in which the situation is represented in a schematic way. Popular modelling techniques are: process model, workflow model, life cycle model.
A method is a systematic approach to achieve a specific result or goal, and offers a description in a cohesive and (scientific) consistent way of the approach that leads to the desired result/ goal. Minimally a method consists of a way of thinking and a way of working. Possible additional components of a method are: management model(s), presentation model(s), support model(s) (prescriptions, instructions, tips, examples, etc.), based on the modelling techniques mentioned above. The meanings of the terms ‘practice’ and ‘model’ are much broader than the term ‘method’.
A framework is an entity between a ‘model’ and a ‘method’. A framework is, or contains, a (not completely detailed) structure or system for the realization of a defined result/goal. Many frameworks comprise one or more models, based on the modelling techniques mentioned above and often based on (best) practices. Compared with methods, frameworks give the users much more freedom regarding the (partial or entire) use of the framework and the use of the models or techniques therein.
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The main difference between syntax analysis and semantic analysis is that syntax analysis takes the tokens generated by the lexical analysis and generates a parse tree while semantic analysis checks whether the parse tree generated by syntax analysis follows the rules of the language.
https://pediaa.com/what-is-the-difference-between-syntax-analysis-and-semantic-analysis/
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