Constraint propagation

In constraint satisfactionlocal consistency conditions are properties of constraint satisfaction problems related to the consistency of subsets of variables or constraints.

They can be used to reduce the search space and make the problem easier to solve. Various kinds of local consistency conditions are leveraged, including node consistencyarc consistencyand path consistency. Every local consistency condition can be enforced by a transformation that changes the problem without changing its solutions. Such a transformation is called constraint propagation.

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Constraint propagation works by reducing domains of variables, strengthening constraints, or creating new ones.

This leads to a reduction of the search space, making the problem easier to solve by some algorithms.

Constraint Propagation for solving Sudoku puzzles

Constraint propagation can also be used as an unsatisfiability checker, incomplete in general but complete in some particular cases. Local consistency conditions can be grouped into various classes. The original local consistency conditions require that every consistent assignment can be consistently extended to another variable. Directional consistency only requires this condition to be satisfied when the other variable is higher than the ones in the assignment, according to a given order.

Relational consistency includes extensions to more than one variable, but this extension is only required to satisfy a given constraint or set of constraints. In this article, a constraint satisfaction problem is defined as a set of variables, a set of domains, and a set of constraints. Variables and domains are associated: the domain of a variable contains all values the variable can take.

A constraint is composed of a sequence of variables, called its scope, and a set of their evaluations, which are the evaluations satisfying the constraint. The constraint satisfaction problems referred to in this article are assumed to be in a special form. A problem is in normalized formrespectively regular formif every sequence of variables is the scope of at most one constraint or exactly one constraint. The assumption of regularity done only for binary constraints leads to the standardized form.

In the figures used in this article, the lack of links between two variables indicate that either no constraint or a constraint satisfied by all values exists between these two variables. The "standard" local consistency conditions all require that all consistent partial evaluations can be extended to another variable in such a way that the resulting assignment is consistent.

A partial evaluation is consistent if it satisfies all constraints whose scope is a subset of the assigned variables. Node consistency requires that every unary constraint on a variable is satisfied by all values in the domain of the variable, and vice versa. This condition can be trivially enforced by reducing the domain of each variable to the values that satisfy all unary constraints on that variable. As a result, unary constraints can be neglected and assumed incorporated into the domains.

This pre-processing step simplifies later stages. A variable of a constraint satisfaction problem is arc-consistent with another one if each of its admissible values are consistent with some admissible value of the second variable. A problem is arc consistent if every variable is arc consistent with every other one.

Arc consistency can also be defined relative to a specific binary constraint: a binary constraint is arc-consistent if every value of one variable has a value of the second variable such that they satisfy the constraint. This definition of arc consistency is similar to the above, but is given specific to a constraint. This difference is especially relevant for non-normalized problems, where the above definition would consider all constraints between two variables while this one considers only a specific one.

If a variable is not arc consistent with another one, it can be made so by removing some values from its domain. This is the form of constraint propagation that enforces arc consistency: it removes, from the domain of the variable, every value that does not correspond to a value of the other variable. This transformation maintains the problem solutions, as the removed values are in no solution anyway. Constraint propagation can make the whole problem arc consistent by repeating this removal for all pairs of variables.

This process might have to consider a given pair of variables more than once. Indeed, removing values from the domain of a variable may cause other variables to become no longer arc consistent with it. A simplistic algorithm would cycle over the pairs of variables, enforcing arc-consistency, repeating the cycle until no domains change for a whole cycle. The AC-3 algorithm improves over this algorithm by ignoring constraints that have not been modified since they were last analyzed.

In particular, it works on a set of constraints that initially contains all of them; at each step, it takes a constraint and enforces arc-consistency; if this operation may have produced a violation of arc-consistency over another constraint, it places it back in the set of constraints to analyze.In artificial intelligence and operations researchconstraint satisfaction is the process of finding a solution to a set of constraints that impose conditions that the variables must satisfy.

The techniques used in constraint satisfaction depend on the kind of constraints being considered. Often used are constraints on a finite domainto the point that constraint satisfaction problems are typically identified with problems based on constraints on a finite domain. Such problems are usually solved via searchin particular a form of backtracking or local search. Constraint propagation are other methods used on such problems; most of them are incomplete in general, that is, they may solve the problem or prove it unsatisfiable, but not always.

Constraint propagation methods are also used in conjunction with search to make a given problem simpler to solve. Other considered kinds of constraints are on real or rational numbers; solving problems on these constraints is done via variable elimination or the simplex algorithm.

During the s and s, embedding of constraints into a programming language were developed. As originally defined in artificial intelligence, constraints enumerate the possible values a set of variables may take in a given world.

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A possible world is a total assignment of values to variables representing a way the world real or imaginary could be. A constraint satisfaction problem on such domain contains a set of variables whose values can only be taken from the domain, and a set of constraints, each constraint specifying the allowed values for a group of variables. A solution to this problem is an evaluation of the variables that satisfies all constraints.

In other words, a solution is a way for assigning a value to each variable in such a way that all constraints are satisfied by these values.

Constraint satisfaction

In some circumstances, there may exist additional requirements: one may be interested not only in the solution and in the fastest or most computationally efficient way to reach it but in how it was reached; e.

This is often the case in logic games such as Sudoku. In practice, constraints are often expressed in compact form, rather than enumerating all the values of the variables that would satisfy the constraint. One of the most used constraints is the obvious one establishing that the values of the affected variables must be all different.

Problems that can be expressed as constraint satisfaction problems are the eight queens puzzlethe Sudoku solving problem and many other logic puzzles, the Boolean satisfiability problemscheduling problems, bounded-error estimation problems and various problems on graphs such as the graph coloring problem. While usually not included in the above definition of a constraint satisfaction problem, arithmetic equations and inequalities bound the values of the variables they contain and can therefore be considered a form of constraints.

Arithmetic equations and inequalities are often not considered within the definition of a "constraint satisfaction problem", which is limited to finite domains. They are however used often in constraint programming. It can be shown that the arithmetic inequalities or equations present in some types of finite logic puzzles such as Futoshiki or Kakuro also known as Cross Sums can be dealt with as non-arithmetic constraints see Pattern-Based Constraint Satisfaction and Logic Puzzles [3].

Constraint satisfaction problems on finite domains are typically solved using a form of search. The most used techniques are variants of backtrackingconstraint propagationand local search.

These techniques are used on problems with nonlinear constraints. Variable elimination and the simplex algorithm are used for solving linear and polynomial equations and inequalities, and problems containing variables with infinite domain. These are typically solved as optimization problems in which the optimized function is the number of violated constraints.You can also paginate, filter, and order your forecasts.

Batch Predictions Last Updated: Monday, 2017-10-30 10:31 A batch prediction provides an easy way to compute a prediction for each instance in a dataset in only one request. Batch predictions are created asynchronously. You can retrieve the associated resource to check the progress and status in a similar fashion to the rest of BigML.

For example, you can set up the "separator" (e. You can read about all the available options below. You can also list all of your batch predictions. Your authentication variable should be set up first as shown above. Example: true importance optional Boolean,default is false Whether to include a column for each of the field importances for model and ensemble predictions.

That will add a column per field, named " importance". All the fields in the dataset Specifies the fields in the dataset to be considered to create the batch prediction.

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That is, when a missing value is found in the input data for a decision node. The options are: 0: last prediction predicts based on the subset of the data which reached the parent of the missing split. Alternatively, you can use ensemble, logisticregression or deepnet arguments.

Local consistency

Otherwise, BigML will predict the class with the higher confidence or probability (depending on the kind). For non-boosted ensembles, there is a third kind available: votes. None of the fields in the dataset Specifies the fields to be included in the csv file.

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It can be a list of field ids or names. It will only have effect if header is true. Example: "Prediction" probabilities optional Boolean,default is false Whether to include the predicted class and all other possible class values for the batch prediction for the classification task.

If enabled, the columns are included after the confidence score. Example: true probability optional Boolean,default is false Whether the probability for each prediction for the classification task should be added. It's 1 by default. This is the usual default in some systems trying to detect anomalies (e. IDS and the like), and other uses of this combiner should probably not rely on our default value. Their use is deprecated, and maintained only for backwards compatibility.

Example: true You can also use curl to customize a new batch prediction. For example, to create a new batch prediction named "my batch prediction", that will not include a header, and will only output the field "000001" together with the confidence for each prediction. Once a batch prediction has been successfully created it will have the following properties.

Creating a batch prediction is a process that can take just a few seconds or a few hours depending on the size of the dataset used as input and on the workload of BigML's systems. The batch prediction goes through a number of states until its finished.The top two are 28 days ago and the bottom two are from this morning. I must clarify that while using the daytime and night time Teatox, I was trying to eat as clean as possible and working out regularly.

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Definitely going to go for the 28 day next time. Also the tea tasted lovely :) quite upset that I've now finished it. I haven't finished my health journey yet, it's just getting started.For example, to create a new batch anomaly score named "my batch anomaly score", that will not include a header, and will only output the field "000001" together with the score for each anomaly score.

Once a batch anomaly score has been successfully created it will have the following properties. Creating a batch anomaly score is a process that can take just a few seconds or a few hours depending on the size of the dataset used as input and on the workload of BigML's systems. The batch anomaly score goes through a number of states until its finished. Through the status field in the batch anomaly score you can determine when it has been fully processed.

Once you delete a batch anomaly score, it is permanently deleted. If you try to delete a batch anomaly score a second time, or a batch anomaly score that does not exist, you will receive a "404 not found" response.

However, if you try to delete a batch anomaly score that is being used at the moment, then BigML. To list all the batch anomaly scores, you can use the batchanomalyscore base URL. By default, only the 20 most recent batch anomaly scores will be returned. You can get your list of batch anomaly scores directly in your browser using your own username and API key with the following links. You can also paginate, filter, and order your batch anomaly scores. Batch Topic Distributions Last Updated: Monday, 2017-10-30 10:31 A batch topic distribution provides an easy way to compute a topic distribution for each instance in a dataset in only one request.

Batch topic distributions are created asynchronously. You can also list all of your batch topic distributions. You can easily create a new batch topic distribution using curl as follows. All the fields in the dataset Specifies the fields in the dataset to be considered to create the batch topic distribution. Example: "my new batch topic distribution" newline optional String,default is "LF" The new line character that you want to get as line break in the generated csv file: "LF", "CRLF".

For example, to create a new batch topic distribution named "my batch topic distribution", that will not include a header, and will only output the field "000001" together with the probability for each topic distribution.

Once a batch topic distribution has been successfully created it will have the following properties. Creating a batch topic distribution is a process that can take just a few seconds or a few hours depending on the size of the dataset used as input and on the workload of BigML's systems. The batch topic distribution goes through a number of states until its finished. Through the status field in the batch topic distribution you can determine when it has been fully processed.

Once you delete a batch topic distribution, it is permanently deleted. If you try to delete a batch topic distribution a second time, or a batch topic distribution that does not exist, you will receive a "404 not found" response.The array represents the number of occurences for each digit from 1 to 9.

Name of the outlier detection test. Currently only value available is grubbs. When name is grubbs, it returns Grubbs Result Object. An outlier present in the data. It is available only when at at least of one of the boolean values in significant is true. Example: 128 description optional A description of the model up to 8192 characters long. Example: true name optional The name you want to give to the new model.

Example: 10 randomize optional Setting this parameter to true will consider only a subset of the possible fields when choosing a split.

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Example: 16 tags optional A list of strings that help classify and index your model. Boosting attribute for the boosted tree.

All the information that you need to recreate or use the model on your own. Specifies the list of ids of the field that the model predicts. More concretely, it contains the training data distribution with key training, and the distribution for the actual prediction values of the tree with key predictions.

Importance is the amount by which each field in the model reduces prediction error, normalized to be between zero and one. Default strategy followed by the model when it finds a missing value. At prediction time you can opt for using proportional.

A dictionary with an entry per field used by the model (not all the fields that were available in the dataset). They follow the same structure as the fields attribute above except that the summary is not present.

A Node Object, a tree-like recursive structure representing the model. Method of choosing best attribute and split point for a given node. For classification models, a number between 0 and 1 that expresses how certain the model is of the prediction.

See the Section on Confidence for more details. Note that for models you might have created using the first versions of BigML this value might be null. An Objective Summary Object summarizes the objective field's distribution at this node. If the objective field is numeric and the number of distinct values is greater than 32.For help text HELP anytime.

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