learned metric to simulate the effect of L1 regularization. In particular, we introduce a data dependent dropout probability as
Now, instead of perturbing Mt−1, we apply dropout to M’ t , i.e. the matrix after the gradient mapping. It is easy to verify that the expectation of the perturbed matrix Mˆ 0 is given by
which is equivalent to the thresholding method stated above. It is straightforward to extend the method to Lp norm
by setting the probability as
Note that when p = 1, it is equivalent to the probability for L1 norm.
Given Q, which is a random matrix with each element from a uniform distribution in [0, 1], we investigate the matrix
It is obvious that the diagonal elements of R are still from the same uniform distribution, while elements in off diagonal are from a triangle distribution with cumulative distribution function as
The dropout probability based on the random matrix R is defined as
First, we consider dropout with the same probability for each item of the metric as for Frobenius norm. Then, the probability of is
Then, we consider dropout with the probability based on the elements as
6.Applying Dropout to Training Data
In the Guassian noise could perform as the trace norm, the external noise may affect the solution. Therefore, we consider dropout as
where is a binary value random variable and
Note that when we perform dropout to the training data according to this strategy, we actually drop the rows and the corresponding…
techniques, and Expert judgment (PMI, 2013, p. 334).
For the data collecting process, the most popular ones are expert interviews, and the Probability distributions, which can describe uncertainty events in the project in the distribution shape figure. The expert interviews are useful since experts are experienced project management professionals and would contribute lots of useful information and data from the past projects (Hulett & Preston, 2000).
It is important to make a specific…
John Gutmann was one of America’s most distinctive photographers. Gutmann was born in Germany where he became an artist. He later fled Germany due to the Nazi’s because he was a Jew. Gutmann moved to San Francisco and re-established himself as a photojournalist captivating the lives of Americans. He mainly took photographs of people who were imperfect like himself because of his Jewish nationality. Gutmann targeted the poor, circus folk, the gay community and the rich. Two of Gutmann’s works are…
The fundamental theorem of Calculus:
The fundamental theorem of calculus asserts the interrelated properties of integration and differentiation. It says that a function when differentiated, can be brought back by integrating (anti-derivative) or a function when integrated, can be brought back by differentiation.
First theorem: Let f be a function that is integrable on [a,x] for each x in [a,b], then let c be such that a≤c≤b and define a new function A as follows,
A(x)=∫_c^x▒f(x)dt, if a≤x≤b.…
Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus evaluate an antiderivative at the upper and lower limits of integration and take the difference. This theorem is separated into two parts. The first part is called the first fundamental theorem of calculus and states that one of the antiderivatives of some function may be obtained as the integral of the function with a variable bound of integration. The second part of the theorem, called the second fundamental theorem of…
It is also
expedient to verify that the selected distribution eectively models the data because anything short
of almost accurate could prove detrimental to future predictions. Hogg and Klugman (1984) serves
as a standard reference for this subject.
Adeleke and Ibiwoye (2011) used these same concepts to model claim sizes in personal line non-
life insurance in Nigeria. They performed analysis of claim size to determine fair premium to
ensure that the premium charged to individual members of the…
Memory and personal identity are an integral part of our lives. These characteristics and traits assist us in the way we make decisions and approach situations. Memory in relation to personal identity is a topic that has been studied by several Philosophers. The question of whether or not memory presupposes identity is a circular one, and therefore makes this question important. To study this, I looked at Parfits theory of Psychological continuity, and how it was seen as problematic due to its…
Materiality and Identity
Megan Holmes’s “Miraculous Images in Renaissance Florence” examines many of the ramifications of materiality. The materiality, an image’s physical properties, has direct impacts on the expression and popularity of immagini miracolose. These sacred images are subjects of miracles throughout the late 13th to 16th centuries. Two of the most important ramifications of materiality include the accessibility of the religious images and manifestation of the miracles. In this…
1. Henri Lebesgue 
Lebesgue is credited for many amazing discoveries to different areas of mathematics. In the area of topology, Lebesgue is known for his covering theorem which is used for finding the dimensions of a set. He is also credited for his work on the Fourier series. He was able to demonstrate that using term by term integration of a series that were Lebesgue integrable functions was always valid and therefore, gave validation to Fourier’s proof of his series.
What is now…
1. What are the least, and most, amount of distinct zeroes of a 7th degree polynomial, given that at least one root is a complex number?
If the equation is 7th degree then it has 7 roots.
Those roots can be complex or real.
Complex roots always come in pairs, so if it has one, then it has 2, the other one being the conjugate of the first one. This in other words, if one complex root is a + bi, then the other complex root is a – bi.
If at least one root were complex, then we would have a…