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Here is my web site; http://Www.hostgator1centcoupon.info/ (support.file1.com) Dynamic topic models are generative models that can be used to analyze the evolution of (unobserved) topics of a collection of documents over time. This family of models was proposed by David Blei and John Lafferty and is an extension to Latent Dirichlet Allocation (LDA) that can handle sequential documents.

In LDA, both the order the words appear in a document and the order the documents appear in the corpus are oblivious to the model. Whereas words are still assumed to be exchangeable, in a dynamic topic model the order of the documents plays a fundamental role. More precisely, the documents are grouped by time slice (e.g.: years) and it is assumed that the documents of each group come from a set of topics that evolved from the set of the previous slice.

Topics

Similarly to LDA and pLSA, in a dynamic topic model, each document is viewed as a mixture of unobserved topics. Furthermore, each topic defines a multinomial distribution over a set of terms. Thus, for each word of each document, a topic is drawn from the mixture and a term is subsequently drawn from the multinomial distribution corresponding to that topic.

The topics, however, evolve over time. For instance, the two most likely terms of a topic at time Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

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This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

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Model

Define

${\alpha }_t$ as the per-document topic distribution at time t.

${\beta }_{t,k}$ as the word distribution of topic k at time t.

${\theta }_{t,d}$ as the topic distribution for document d in time t,

$z_{t,d,n}$ as the topic for the nth word in document d in time t, and

$w_{t,d,n}$ as the specific word.

In this model, the multinomial distributions ${\alpha }_{t+1}$ and ${\beta }_{t+1,k}$ are generated from ${\alpha }_t$ and ${\beta }_{t,k}$, respectively. Even though multinomial distributions are usually written in terms of the mean parameters, representing them in terms of the natural parameters is better in the context of dynamic topic models.

The former representation has some disadvantages due to the fact that the parameters are constrained to be non-negative and sum to one. When defining the evolution of these distributions, one would need to assure that such constraints were satisfied. Since both distributions are in the exponential family, one solution to this problem is to represent them in terms of the natural parameters, that can assume any real value and can be individually changed.

Using the natural parameterization, the dynamics of the topic model are given by

${\beta }_{t,k}|{\beta }_{t-1,k}\sim N({\beta }_{t-1,k},{\sigma }^{2}I)$

and

${\alpha }_t|{\alpha }_{t-1}\sim N({\alpha }_{t-1},{\delta }^{2}I)$.

The generative process at time slice 't' is therefore:

1. Draw topics ${\beta }_{t,k}|{\beta }_{t-1,k}\sim N({\beta }_{t-1,k},{\sigma }^{2}I)\mathrm{\forall }k$
2. Draw mixture model ${\alpha }_t|{\alpha }_{t-1}\sim N({\alpha }_{t-1},{\delta }^{2}I)$
3. For each document:
   1. Draw ${\eta }_{t,d}\sim N({\alpha }_t,a^{2}I)$
   2. For each word:
      1. Draw topic $Z_{t,d,n}\sim \text{<mrow data-mjx-texclass="ORD">Mult</mrow>}(\pi ({\eta }_{t,d}))$
      2. Draw word $W_{t,d,n}\sim \text{<mrow data-mjx-texclass="ORD">Mult</mrow>}(\pi ({\beta }_{t,Z_{t,d,n}}))$

where $\pi (x)$ is a mapping from the natural parameterization x to the mean parameterization, namely

$\pi (x_i)=\frac{\exp (x_i)}{\sum _i\exp (x_i)}$.

Inference

In the dynamic topic model, only $W_{t,d,n}$ is observable. Learning the other parameters constitutes an inference problem. Blei and Lafferty argue that applying Gibbs sampling to do inference in this model is more difficult than in static models, due to the nonconjugacy of the Gaussian and multinomial distributions. They propose the use of variational methods, in particular, the Variational Kalman Filtering and the Variational Wavelet Regression.

Application

In the original paper, a dynamic topic model is applied to the corpus of Science articles published between 1881 to 1999 aiming to show that this method can be used to analyze the trends of word usage inside topics. The authors also show that the model trained with past documents is able to fit documents of an incoming year better than LDA.

A continuous dynamic topic model was developed by Wang et al. and applied to predict the timestamp of documents.

References

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