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A portion of each payment is for the interest while the remaining amount is applied towards the principal balance. During initial loan period, a large portion of each payment is devoted to interest.

With passage of time, larger portions pay down the principal. The payment schedule also shows the intermediate outstanding balance for each year which will be carried over to the next year.

Want to make part prepayments to shorten your home loan schedule and reduce your total interest outgo? Loan amount and loan tenure, two components required to calculate the EMI are under your control; i.

As a borrower, you should consider the two extreme possibilities of increase and decrease in the rate of interest and calculate your EMI under these two conditions.

Such calculation will help you decide how much EMI is affordable, how long your loan tenure should be and how much you should borrow.

Consider this situation and calculate your EMI. In this situation, your EMI will come down or you may opt to shorten the loan tenure.

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EM Calculation \u0026 Current CalculationMarital Status. Sexual History. Occupational History. Use of Drugs, Alchohol, or Tobacco. Extent of Education. Current Employment.

Patient History unobtainable. Chest, including breasts and axillae. Genitalia, groin, buttocks. Back, including spine. Right upper extremity.

Left upper extremity. Right lower extremity. Left lower extremity. Ears, nose, mouth, and throat. Detailed exam.

General appearance of patient. Inspection of conjunctivae and lids. Examination of pupils and irises. Ophthalmoscopic examination of optic discs.

External inspection of ears and nose. Otoscopic examination of external auditory canals and tympanic membranes. Assessment of hearing. Inspection of nasal mucosa, septum and turbinate's.

Inspection of lips, teeth, and gums. Examination of oropharynx: oral mucosa, salivary glands, hard and soft palates, tongue, tonsils, and posterior pharynx.

Examination of Neck. Examination of Thyroid. Assessment of respiratory effort. Percussion of chest. Palpitation of chest. Auscultation of lungs.

Palpitation of heart. Auscultation of heart with notation of abnormal sounds and murmurs. Examination of carotid arteries. Examination of abdominal aorta.

Examination of femoral arteries. Examination of pedal pulses. Inspection of breasts. Palpation of breasts and axillae.

Examination of abdomen. Examination of liver and spleen. Examination for presence or absence of hernia. Examine anus, perineum, and rectum.

Obtain stool sample for occult blood test when indicated. Examine the scrotal contents. Examination of penis. Digital rectal examination of prostate gland.

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Inspection of teeth, gums and palate. Inspection of oral mucosa with notation of presence of pallor or cyanosis.

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Measurement of blood pressure in two or more extremities when indicated. Examination of Carotid arteries. Examination of Abdominal aorta.

Examination of Femoral arteries. Examination of Pedal pulses. Examination of abdomen with notation of presence of masses or tenderness.

Obtain stool sample for occult blood from patients who are being considered for thrombolytic or anticoagulant therapy.

Examination of the back with notation of kyphosis or scoliosis. Assessment of muscle strength and tone. Inspection and palpation of digits and nails.

Brief assessment of mental status including: Orientation to time, place and person. Brief assessment of mental status including: Mood and affect.

Assessment of ability to communicate. Inspection of head and face. Examination of salivary glands. Assessment of facial strength. Test ocular motility including primary gaze alignment.

Otoscopic examination of external auditory canals and tympanic membranes including pneumo-otoscopy with notation of mobility of membranes.

Assessment of hearing with tuning forks and clinical speech reception thresholds. Inspection of nasal mucosa, septum and turbinates. Inspection of lips, teeth and gums.

Examination of oropharynx: oral mucosa, hard and soft palates, tongue, tonsils and posterior pharynx.

Inspection of pharyngeal walls and pyriform sinuses. Examination by mirror of larynx including the condition of the epiglottis, false vocal cords, true vocal cords and mobility of larynx.

Examination by mirror of nasopharynx including appearance of the mucosa, adenoids, posterior choanae and Eustachian tubes. Examination of neck.

Auscultation of Auscultation of lungs. Examination of peripheral vascular system by observation. Test cranial nerves with notation of any deficits.

Brief assessment of mental status including: Orientation to time, place, and person. Mood and affect. Eye Exam 97 Eyes Test visual acuity. Gross visual field testing by confrontation.

Inspection of bulbar and palpebral conjunctivae. Examination of ocular adnexae including lids e. Slit lamp examination of the corneas including epithelium, stroma, endothelium, and tear film.

Slit lamp examination of the anterior chambers including depth, cells, and flare. Slit lamp exam of lenses incl.

Measurement of intraocular pressures. Opthalmoscopic exam of posterior segments including retina and vessels.

Genitourinary Exam 97 Constitutional Measurement of any three vital signs. Inspection of anus and perineum. Examination of genitalia including: Scrotum.

One can simply pick arbitrary values for one of the two sets of unknowns, use them to estimate the second set, then use these new values to find a better estimate of the first set, and then keep alternating between the two until the resulting values both converge to fixed points.

It's not obvious that this will work, but it can be proven that in this context it does, and that the derivative of the likelihood is arbitrarily close to zero at that point, which in turn means that the point is either a maximum or a saddle point.

Some likelihoods also have singularities in them, i. For example, one of the solutions that may be found by EM in a mixture model involves setting one of the components to have zero variance and the mean parameter for the same component to be equal to one of the data points.

However, this quantity is often intractable e. The EM algorithm seeks to find the MLE of the marginal likelihood by iteratively applying these two steps:.

The motive is as follows. Speaking of an expectation E step is a bit of a misnomer. What are calculated in the first step are the fixed, data-dependent parameters of the function Q.

Once the parameters of Q are known, it is fully determined and is maximized in the second M step of an EM algorithm.

Although an EM iteration does increase the observed data i. For multimodal distributions , this means that an EM algorithm may converge to a local maximum of the observed data likelihood function, depending on starting values.

EM is especially useful when the likelihood is an exponential family : the E step becomes the sum of expectations of sufficient statistics , and the M step involves maximizing a linear function.

In such a case, it is usually possible to derive closed-form expression updates for each step, using the Sundberg formula published by Rolf Sundberg using unpublished results of Per Martin-Löf and Anders Martin-Löf.

Other methods exist to find maximum likelihood estimates, such as gradient descent , conjugate gradient , or variants of the Gauss—Newton algorithm.

Here it is shown that improvements to the former imply improvements to the latter. The left-hand side is the expectation of a constant, so we get:.

The EM algorithm can be viewed as two alternating maximization steps, that is, as an example of coordinate descent.

This function can be written as. EM is frequently used for parameter estimation of mixed models , [17] [18] notably in quantitative genetics.

In psychometrics , EM is almost indispensable for estimating item parameters and latent abilities of item response theory models.

With the ability to deal with missing data and observe unidentified variables, EM is becoming a useful tool to price and manage risk of a portfolio.

The EM algorithm and its faster variant ordered subset expectation maximization is also widely used in medical image reconstruction, especially in positron emission tomography , single photon emission computed tomography , and x-ray computed tomography.

See below for other faster variants of EM. In structural engineering , the Structural Identification using Expectation Maximization STRIDE [20] algorithm is an output-only method for identifying natural vibration properties of a structural system using sensor data see Operational Modal Analysis.

EM is also frequently used for data clustering , computer vision and in machine learning. In natural language processing , two prominent instances of the algorithm are the Baum—Welch algorithm for hidden Markov models , and the inside-outside algorithm for unsupervised induction of probabilistic context-free grammars.

A Kalman filter is typically used for on-line state estimation and a minimum-variance smoother may be employed for off-line or batch state estimation.

However, these minimum-variance solutions require estimates of the state-space model parameters. EM algorithms can be used for solving joint state and parameter estimation problems.

Suppose that a Kalman filter or minimum-variance smoother operates on measurements of a single-input-single-output system that possess additive white noise.

An updated measurement noise variance estimate can be obtained from the maximum likelihood calculation. The above update can also be applied to updating a Poisson measurement noise intensity.

Similarly, for a first-order auto-regressive process, an updated process noise variance estimate can be calculated by. The updated model coefficient estimate is obtained via.

The convergence of parameter estimates such as those above are well studied. A number of methods have been proposed to accelerate the sometimes slow convergence of the EM algorithm, such as those using conjugate gradient and modified Newton's methods Newton—Raphson.

This idea is further extended in generalized expectation maximization GEM algorithm, in which is sought only an increase in the objective function F for both the E step and M step as described in the As a maximization-maximization procedure section.

The Q-function used in the EM algorithm is based on the log likelihood. Therefore, it is regarded as the log-EM algorithm. Obtaining this Q-function is a generalized E step.

Its maximization is a generalized M step. No computation of gradient or Hessian matrix is needed. EM is a partially non-Bayesian, maximum likelihood method.

In this paradigm, the distinction between the E and M steps disappears. Now, k steps per iteration are needed, where k is the number of latent variables.

For graphical models this is easy to do as each variable's new Q depends only on its Markov blanket , so local message passing can be used for efficient inference.

In information geometry , the E step and the M step are interpreted as projections under dual affine connections , called the e-connection and the m-connection; the Kullback—Leibler divergence can also be understood in these terms.

The aim is to estimate the unknown parameters representing the mixing value between the Gaussians and the means and covariances of each:.

The inner sum thus reduces to one term. These are called the "membership probabilities", which are normally considered the output of the E step although this is not the Q function of below.

This has the same form as the MLE for the binomial distribution , so. The algorithm illustrated above can be generalized for mixtures of more than two multivariate normal distributions.

The EM algorithm has been implemented in the case where an underlying linear regression model exists explaining the variation of some quantity, but where the values actually observed are censored or truncated versions of those represented in the model.

EM typically converges to a local optimum, not necessarily the global optimum, with no bound on the convergence rate in general.

It is possible that it can be arbitrarily poor in high dimensions and there can be an exponential number of local optima. Hence, a need exists for alternative methods for guaranteed learning, especially in the high-dimensional setting.

Alternatives to EM exist with better guarantees for consistency, which are termed moment-based approaches [34] or the so-called spectral techniques [35] [36] [ citation needed ].

Moment-based approaches to learning the parameters of a probabilistic model are of increasing interest recently since they enjoy guarantees such as global convergence under certain conditions unlike EM which is often plagued by the issue of getting stuck in local optima.

Algorithms with guarantees for learning can be derived for a number of important models such as mixture models, HMMs etc.

For these spectral methods, no spurious local optima occur, and the true parameters can be consistently estimated under some regularity conditions [ citation needed ].

From Wikipedia, the free encyclopedia. Iterative method for finding maximum likelihood estimates in statistical models. Dimensionality reduction.

Structured prediction. Graphical models Bayes net Conditional random field Hidden Markov. Anomaly detection.

Artificial neural network. Reinforcement learning. Machine-learning venues. Glossary of artificial intelligence. Related articles.

List of datasets for machine-learning research Outline of machine learning.

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