Percolation critical exponents

My name is Jestine (34 years old) and my hobbies are Origami and Microscopy.

Here is my web site; http://Www.hostgator1centcoupon.info/ (support.file1.com) The Binary Independence Model (BIM) is a probabilistic information retrieval technique that makes some simple assumptions to make the estimation of document/query similarity probability feasible.

Definitions

The Binary Independence Assumption is that documents are binary vectors. That is, only the presence or absence of terms in documents are recorded. Terms are independently distributed in the set of relevant documents and they are also independently distributed in the set of irrelevant documents. The representation is an ordered set of Boolean variables. That is, the representation of a document or query is a vector with one Boolean element for each term under consideration. More specifically, a document is represented by a vector d = (x₁, ..., x_m) where x_t=1 if term t is present in the document d and x_t=0 if it's not. Many documents can have the same vector representation with this simplification. Queries are represented in a similar way. "Independence" signifies that terms in the document are considered independently from each other and no association between terms is modeled. This assumption is very limiting, but it has been shown that it gives good enough results for many situations. This independence is the "naive" assumption of a Naive Bayes classifier, where properties that imply each other are nonetheless treated as independent for the sake of simplicity. This assumption allows the representation to be treated as an instance of a Vector space model by considering each term as a value of 0 or 1 along a dimension orthogonal to the dimensions used for the other terms.

The probability P(R|d,q) that a document is relevant derives from the probability of relevance of the terms vector of that document P(R|x,q). By using the Bayes rule we get:

$P(R|x,q)={\frac {P(x|R,q)*P(R|q)}{P(x|q)}}$

where P(x|R=1,q) and P(x|R=0,q) are the probabilities of retrieving a relevant or nonrelevant document, respectively. If so, then that document's representation is x. The exact probabilities can not be known beforehand, so use estimates from statistics about the collection of documents must be used.

P(R=1|q) and P(R=0|q) indicate the previous probability of retrieving a relevant or nonrelevant document respectively for a query q. If, for instance, we knew the percentage of relevant documents in the collection, then we could use it to estimate these probabilities. Since a document is either relevant or nonrelevant to a query we have that:

$P(R=1|x,q)+P(R=0|x,q)=1$

Query Terms Weighting

Given a binary query and the dot product as the similarity function between a document and a query, the problem is to assign weights to the terms in the query such that the retrieval effectiveness will be high. Let $p_{i}$ and $q_{i}$ be the probability that a relevant document and an irrelevant document has the $i^{th}$ term respectively. Yu and Salton, who first introduce BIM, propose that the weight of the $i^{th}$ term is an increasing function of $Y_{i}={\frac {p_{i}*(1-q_{i})}{(1-p_{i})*q_{i}}}$. Thus, if $Y_{i}$ is higher than $Y_{j}$, the weight of term $i$ will be higher than that of term $j$. Yu and Salton showed that such a weight assignment to query terms yields better retrieval effectiveness than if query terms are equally weighted. Robertson and Sparck later showed that if the $i^{th}$ term is assigned the weight of $logY_{i}$, then optimal retrieval effectiveness is obtained under the Binary Independence Assumption.

The Binary Independence Model was introduced by Yu and Salton. The name Binary Independence Model was coined by Robertson and Sparck.

Recent work

Wu et al. proposed a new probabilistic retrieval model which weights terms according to their contexts in documents. The term weighting function they used is similar to the language model and the binary independence model.

Roelleke et al. investigates the probabilistic relational implementations of BIM under the use of probabilistic relational algebra for the integration of Information Retrieval in databases. This work surges as a result of the interest shown by Surajit et al. in applying the knowledge of probabilistic models for information retrieval in structured data, to investigate the problem of ranking the answers to a database query when many tuples are returned.

Zhao and Callan (2010) showed a connection between $p_{i}$, the probability of a term appearing in relevant documents, and the vocabulary mismatch problem. This leads to effective ways of predicting the $p_{i}$ probability for test queries without relevance judgments using training queries with known relevance judgments. Term weighting using this probability could potentially lead to 50-80% gain in retrieval performance over stronger baseline retrieval models such as Language Modeling with perfect estimates of the probability. Further developments following this line of idea points at the Boolean Conjunctive Normal Form expansion technique which could lead to 50-300% gain over unexpanded keyword retrieval.

See also

• Bag of words model

Further reading

• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.