I am reading the Bishop Pattern Recognition and Machine Learning and am on section 9.3 An Alternative View on EM:  I am confused as to how Bishop obtains the expression $Q(\theta, \theta^{old}) = \sum_{Z}p(Z | C, \theta^{old}) lnp(X , Z | \theta)$  Thank you for insight!  ANSWER:  In the method of maximum likelihood, we're generally interested in p(X|θ), or equivalently logp(X|θ). We seek a θ that makes this quantity most likely.  However, in our model, in addition to observations X we have latent variable(s) Z which we haven't observed but we have some idea of what it could be (we've elsewhere described a probability distribution guessing Z). So, we're now interested in p(X,Z|θ), or equivalently logp(X,Z|θ), instead of just choosing a θ to maximize p(X|θ).  Yet it's hard to find the θ that maximizes logp(X,Z|θ) if we don't even know what Z is. Instead, we seek the θ that maximizes logp(X,Z|θ) weighted over our distribution of what Z might be.
While im going through the derivation of E step in EM algorithm for pLSA, i came across the following derivation . Could anyone explain me how the following step is derived.   $\sum_z q(z) log \frac{P(X|z,\theta)P(z|\theta)}{q(z)}  = \sum_z q(z) log \frac{P(z|X,\theta)P(X,\theta)}{q(z)} $
The number of 5-digit numbers such that their sum of digits is even is? I tried this problem by counting the number of 5-digit numbers and then dividing it by 2 just like we do for three digits. Please help. Thank you. System freezes completely with Intel Bay Trail How do I scan for viruses with ClamAV? These wonderful icon overlays that give you useful information in the Windows Explorer are not showing up.   It's the most annoying with Dropbox (I already read ). I just tried reinstalling Dropbox - no help. I have this problem also with the  so I don't think that it is a dropbox problem specifically; and something is wrong in my OS. The OS is actually a pretty fresh clean-install...  OS: Win8 Pro 64-bit. I have got a specific folder located in "/home/.../reboot/".  I have a series of users that require read-only access to the ever changing files within.  My problem is that the same users are not authorized to view any of the parent directory files.  Right now, the only thing I have in place is that their starting folder is at "/home/.../reboot/" by changing the etc/passwd file; and I need to block all access to other folders.  How could I only give them access to this directory? How to show that Klein four-group is a normal subgroup of the alternating group $A_4$ Transformer VA Ratings, Power factor, and Pulsed current What exactly goes into a transformer's VA rating? At a fundamental level it seems that there has to be a limit to what the VA rating can represent.  For example if I draw 2 Amps-RMS from the secondary of a 30VA rated transformer at 15 Vrms this makes sense as the maximum Complex Power I can draw. Still, at a power factor of 1 my maximum current in the transformer would be sqrt(2) * 2 Amps.   But what if my power factor is abysmally low (ie in a DC rectifier) due to harmonic distortion and while I still draw 2A-RMS I have brief current spikes of 15 Amps? Surely the transformer's magnetics couldn't handle these spikes as I'd expect the core would saturate.  My question is what is the practical limit for VA ratings of transformers? Would brief current spikes that reduce to only 2A-RMS in this case be fine? Obviously the secondary/primary copper losses play a part in the rating but how do the magnetics factor in?  I ask this because I am designing a simple bench power supply using a 125VA transformer with a 24Vrms secondary and am trying to figure out how much power I can draw before the current spikes into the inductor are too much for the transformer. I also don't want to have to resort to active PFC as I don't want to risk messing up any HVAC PCB design.  Thank you How much money do I need to show as proof of support when applying for a UK Standard Visitor visa? Omitting "and" in a sentence He called her, emailed her, texted her, tweeted her—all to no use.   Strictly speaking, I would need to write texted her and tweeted her, but I'm omitting and to convey a rhythm and sense of urgency. What do you call this kind of construction, and is it accepted grammar (at least for creative writing, if not in an academic context)? Clipping raster with vector boundaries using QGIS In QGIS I would like to clip a raster precipitation layer using an admin boundary layer that is vector data. However the Geoprocessing tools seem to be usable only for vector data. How can I clip this precipitation layer? Is there an English phrase for an inability to actually *leave* already? There is a Hungarian expression, küszöbgörcs, which literally means "threshold-cramp", and is used to describe that long conversation you have in the entryway, with all the guests awkwardly holding their coats and purses, and every so often somebody says something like "Ok, we really have to leave now, but just one more thing...", and then the conversation is good for another half an hour at least.  I've searched in vain for an equivalent idiom in English, yet I feel sure it must exist: I know English speakers are equally susceptible to this malady, it's not a uniquely Hungarian thing. I will sometimes use literal translations, like the aforementioned threshold-cramp (or doorway-spasm), but then I need to explain it, and that's less than satisfactory. (Plus it leads to more threshold cramping.) Cannot get to a new line by hitting Enter I am using a Mac machine.  I asked a question, and then, someone answered it.    I clicked "Edit" to add a comment, and I would like to press Enter to go to a new line, but doing so submitted my comment and ended the edit instead. Can infinitely many primes lie over a prime? Here is the .  Picture:   It's nothing special but I cant figure out why I get problems rigging this mesh. It would be important and a great Help! Thanks for reading and I know there are a lot of guides answering this question but I tried all and it doesn't seem to work. Recovering a accidently deleted file in Ubuntu I'm using ubuntu 9.10 and accidently deleted a specific file within a directory on my system. I checked in the Trash bin and could not locate the file. I deleted it 10mins ago, are there any tools available that I can recovery this file? It's a really important file.  Any help would be highly appreciated  My partition is ext4 Python interpreter error, x takes no arguments (1 given) Is there a 2D generalization of the coefficient of restitution? The  characterizes a collision in one dimension by relating the initial and final speeds of the particles involved,  $$C_R = -\frac{v_{2f} - v_{1f}}{v_{2i} - v_{1i}}$$   In a 2D collision, the velocity can be split into components parallel and perpendicular to the "plane of collision" (the plane tangent to the two objects' surfaces at their contact point), and the equation above applies to the perpendicular components of the velocities only. One could write  $$\begin{pmatrix}v_{2f\shortparallel} - v_{1f\shortparallel} \\ v_{2f\perp} - v_{1f\perp}\end{pmatrix} = \begin{pmatrix}1 &amp; 0 \\ 0 &amp; -C_R\end{pmatrix}\begin{pmatrix}v_{2i\shortparallel} - v_{1i\shortparallel} \\ v_{2i\perp} - v_{1i\perp}\end{pmatrix}$$   My question is, is it useful (i.e. does it produce a more accurate description of realistic 2D collisions) to generalize that matrix? Perhaps by allowing the top left element to be unequal to 1, or allowing nonzero off-diagonal elements? Or is there some nonlinear relation that works better?  As usual, if you know of any relevant published research, references would be much appreciated. How to make child process die after parent exits? Suppose I have a process which spawns exactly one child process. Now when the parent process exits for whatever reason (normally or abnormally, by kill, ^C, assert failure or anything else) I want the child process to die. How to do that correctly?    Some similar question on stackoverflow:   (asked earlier)  (asked later)      Some similar question on stackoverflow for Windows: "In" vs. "after" for future talk How to disable Import option in LibreOffice Calc while pasting text in a cell? I'm making a table in which I have to copy few lines from pdf to a table. I'm using LibreOffice calc for table making purpose. Problem is that even though I am copying simple text from the pdf, when I paste it to LibreOffice, Import Option keeps on poping up(randomly-sometimes it pop up sometime it does't). And due to this pasted text's font size also very small. Desired result is that when I paste the text in the cell, it just got pasted in the cell, without any time wasting popup which also disturbs the font size. Same question is asked here but no solution.